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A triangle can be drawn if the hypotenuse and a _____ in the case of a right-angled triangle.- a)base
- b)hypotenuse
- c)leg
- d)None of these
Correct answer is option 'C'. Can you explain this answer?
A triangle can be drawn if the hypotenuse and a _____ in the case of a right-angled triangle.
a)
base
b)
hypotenuse
c)
leg
d)
None of these
|
Malini bajaj answered |
Explanation:
A right-angled triangle is a triangle in which one of the angles is a right angle (90 degrees). The side opposite to the right angle is called the hypotenuse, and the other two sides are called legs. To draw a triangle, you need at least three sides or two sides and an angle. In the case of a right-angled triangle, if you know the length of the hypotenuse and one leg, you can draw the triangle.
Why option C is correct:
The correct answer is option C, leg. This is because if you know the length of the hypotenuse and one leg, you can use the Pythagorean theorem to find the length of the other leg. The Pythagorean theorem states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides. So, if you know the length of the hypotenuse (c) and one leg (a), you can find the length of the other leg (b) using the following formula:
b = √(c^2 - a^2)
Once you know the length of all three sides, you can draw the triangle.
Example:
Suppose you want to draw a right-angled triangle with a hypotenuse of length 5 units and one leg of length 3 units. To find the length of the other leg, you can use the Pythagorean theorem:
b = √(c^2 - a^2)
b = √(5^2 - 3^2)
b = √(25 - 9)
b = √16
b = 4
So, the length of the other leg is 4 units. Now that you know the length of all three sides, you can draw the triangle.
A right-angled triangle is a triangle in which one of the angles is a right angle (90 degrees). The side opposite to the right angle is called the hypotenuse, and the other two sides are called legs. To draw a triangle, you need at least three sides or two sides and an angle. In the case of a right-angled triangle, if you know the length of the hypotenuse and one leg, you can draw the triangle.
Why option C is correct:
The correct answer is option C, leg. This is because if you know the length of the hypotenuse and one leg, you can use the Pythagorean theorem to find the length of the other leg. The Pythagorean theorem states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides. So, if you know the length of the hypotenuse (c) and one leg (a), you can find the length of the other leg (b) using the following formula:
b = √(c^2 - a^2)
Once you know the length of all three sides, you can draw the triangle.
Example:
Suppose you want to draw a right-angled triangle with a hypotenuse of length 5 units and one leg of length 3 units. To find the length of the other leg, you can use the Pythagorean theorem:
b = √(c^2 - a^2)
b = √(5^2 - 3^2)
b = √(25 - 9)
b = √16
b = 4
So, the length of the other leg is 4 units. Now that you know the length of all three sides, you can draw the triangle.
A triangle in which two sides are of equal lengths is called _______________.- a)equilateral
- b)scalene
- c)isosceles
- d)acute-angled
- e)
Correct answer is option 'C'. Can you explain this answer?
A triangle in which two sides are of equal lengths is called _______________.
a)
equilateral
b)
scalene
c)
isosceles
d)
acute-angled
e)
|
Torcia Education answered |
In geometry, an isosceles triangle is a triangle that has two sides of equal length. Sometimes it is specified as having exactly two sides of equal length, and sometimes as having at least two sides of equal length, the latter version thus including the equilateral triangle as a special case
A simple closed curve made up of only line segments is called a _____.
- a)angle
- b)polygon
- c)quadrilateral
- d)None of these
Correct answer is option 'B'. Can you explain this answer?
A simple closed curve made up of only line segments is called a _____.
a)
angle
b)
polygon
c)
quadrilateral
d)
None of these
|
Kajol jain answered |
The correct answer is option 'B' - polygon.
A polygon is a simple closed curve made of three or more line segments. It is a two-dimensional shape with straight sides. The word "polygon" comes from the Greek words "poly" meaning "many" and "gonia" meaning "angle." A polygon can have any number of sides, but it must have at least three sides to be considered a polygon.
Properties of a Polygon:
1. Sides: A polygon has straight sides, which are line segments. Each side connects two vertices (corners) of the polygon.
2. Vertices: The corners of a polygon are called vertices. Each vertex is the endpoint of two sides.
3. Interior Angles: The interior angles of a polygon are the angles formed inside the shape. The sum of the interior angles of a polygon with n sides can be calculated using the formula (n-2) * 180 degrees.
4. Exterior Angles: The exterior angles of a polygon are the angles formed outside the shape. The sum of the exterior angles of any polygon is always 360 degrees.
5. Diagonals: Diagonals are line segments that connect any two non-adjacent vertices of a polygon. The number of diagonals in a polygon can be found using the formula n * (n-3) / 2, where n is the number of sides.
6. Convex and Concave: A polygon can be convex or concave. A convex polygon has all interior angles less than 180 degrees, while a concave polygon has at least one interior angle greater than 180 degrees.
Examples of Polygons:
- Triangle: A triangle is a polygon with three sides and three vertices.
- Quadrilateral: A quadrilateral is a polygon with four sides and four vertices.
- Pentagon: A pentagon is a polygon with five sides and five vertices.
- Hexagon: A hexagon is a polygon with six sides and six vertices.
- Octagon: An octagon is a polygon with eight sides and eight vertices.
In conclusion, a polygon is a simple closed curve made of three or more line segments. It is a fundamental concept in geometry and has various properties and classifications based on the number of sides and angles it possesses.
A polygon is a simple closed curve made of three or more line segments. It is a two-dimensional shape with straight sides. The word "polygon" comes from the Greek words "poly" meaning "many" and "gonia" meaning "angle." A polygon can have any number of sides, but it must have at least three sides to be considered a polygon.
Properties of a Polygon:
1. Sides: A polygon has straight sides, which are line segments. Each side connects two vertices (corners) of the polygon.
2. Vertices: The corners of a polygon are called vertices. Each vertex is the endpoint of two sides.
3. Interior Angles: The interior angles of a polygon are the angles formed inside the shape. The sum of the interior angles of a polygon with n sides can be calculated using the formula (n-2) * 180 degrees.
4. Exterior Angles: The exterior angles of a polygon are the angles formed outside the shape. The sum of the exterior angles of any polygon is always 360 degrees.
5. Diagonals: Diagonals are line segments that connect any two non-adjacent vertices of a polygon. The number of diagonals in a polygon can be found using the formula n * (n-3) / 2, where n is the number of sides.
6. Convex and Concave: A polygon can be convex or concave. A convex polygon has all interior angles less than 180 degrees, while a concave polygon has at least one interior angle greater than 180 degrees.
Examples of Polygons:
- Triangle: A triangle is a polygon with three sides and three vertices.
- Quadrilateral: A quadrilateral is a polygon with four sides and four vertices.
- Pentagon: A pentagon is a polygon with five sides and five vertices.
- Hexagon: A hexagon is a polygon with six sides and six vertices.
- Octagon: An octagon is a polygon with eight sides and eight vertices.
In conclusion, a polygon is a simple closed curve made of three or more line segments. It is a fundamental concept in geometry and has various properties and classifications based on the number of sides and angles it possesses.
A triangle can be drawn if ______ sides given.- a)3
- b)1
- c)2
- d)none of these
Correct answer is option 'A'. Can you explain this answer?
A triangle can be drawn if ______ sides given.
a)
3
b)
1
c)
2
d)
none of these
|
Kunal Chakraborty answered |
Introduction:
A triangle is a closed figure with three sides. To draw a triangle, we need to have information about the lengths of its sides. In this question, we are asked to determine the minimum number of sides required to draw a triangle.
Explanation:
In order to draw a triangle, we need to consider the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
Triangle Inequality Theorem:
According to the triangle inequality theorem, for any triangle with sides of lengths a, b, and c:
a + b > c
b + c > a
c + a > b
Options:
Let's analyze each option to determine if a triangle can be drawn with that number of sides:
a) 3 sides: If we have the lengths of all three sides, we can apply the triangle inequality theorem to check if a triangle can be drawn. Since all three conditions of the triangle inequality theorem are met, we can draw a triangle with the given side lengths.
b) 1 side: If we have only one side length, we cannot determine a triangle. We need at least two more side lengths to apply the triangle inequality theorem.
c) 2 sides: If we have the lengths of two sides, we can apply the triangle inequality theorem to check if a triangle can be drawn. In this case, we can determine a triangle by ensuring that the sum of the lengths of the two sides is greater than the length of the third side.
d) None of these: This option implies that no information about the sides is given. Without any side lengths, we cannot determine if a triangle can be drawn.
Conclusion:
Based on the analysis, we can conclude that a triangle can be drawn if we have the lengths of all three sides (option a).
A triangle is a closed figure with three sides. To draw a triangle, we need to have information about the lengths of its sides. In this question, we are asked to determine the minimum number of sides required to draw a triangle.
Explanation:
In order to draw a triangle, we need to consider the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
Triangle Inequality Theorem:
According to the triangle inequality theorem, for any triangle with sides of lengths a, b, and c:
a + b > c
b + c > a
c + a > b
Options:
Let's analyze each option to determine if a triangle can be drawn with that number of sides:
a) 3 sides: If we have the lengths of all three sides, we can apply the triangle inequality theorem to check if a triangle can be drawn. Since all three conditions of the triangle inequality theorem are met, we can draw a triangle with the given side lengths.
b) 1 side: If we have only one side length, we cannot determine a triangle. We need at least two more side lengths to apply the triangle inequality theorem.
c) 2 sides: If we have the lengths of two sides, we can apply the triangle inequality theorem to check if a triangle can be drawn. In this case, we can determine a triangle by ensuring that the sum of the lengths of the two sides is greater than the length of the third side.
d) None of these: This option implies that no information about the sides is given. Without any side lengths, we cannot determine if a triangle can be drawn.
Conclusion:
Based on the analysis, we can conclude that a triangle can be drawn if we have the lengths of all three sides (option a).
ΔABC is right-angled at C. If AC = 5 cm and BC = 12 cm find the length of AB.- a)17 cm
- b)7 cm
- c)13 cm
- d)None of these
Correct answer is option 'C'. Can you explain this answer?
ΔABC is right-angled at C. If AC = 5 cm and BC = 12 cm find the length of AB.
a)
17 cm
b)
7 cm
c)
13 cm
d)
None of these
|
Anand Choudhury answered |
Given that AC=12cm and BC=5cm,
We can find out the value of AB by using Pythagoras theorum,
that is AB^2=BC^2+AC^2
AB^2=12^2+5^2
AB^2=144+25
AB^2=169
AB=√169
AB=13cm
The sum of the lengths of any two sides of a triangle is _____________ the third side of the triangle.- a)less than
- b)doubled
- c)greater than
- d)half
Correct answer is option 'C'. Can you explain this answer?
The sum of the lengths of any two sides of a triangle is _____________ the third side of the triangle.
a)
less than
b)
doubled
c)
greater than
d)
half
|
|
Shadow 😇🤍 answered |
The sum of the lengths of any two sides of a triangle is greater than the length of the third side. C is correct
ΔPQR is a triangle right-angled at P. If PQ = 3 cm and PR = 4 cm, find QR.- a)3 cm
- b)7 cm
- c)5 cm
- d)8 cm
Correct answer is option 'C'. Can you explain this answer?
ΔPQR is a triangle right-angled at P. If PQ = 3 cm and PR = 4 cm, find QR.
a)
3 cm
b)
7 cm
c)
5 cm
d)
8 cm
|
Swati shukla answered |
There are several possible ways to solve this equation. Here are a few methods:
1. Graphing: Plot the graphs of y = 2x and y = -x^2 + 4. The solution(s) will be the x-coordinates of the points where the two graphs intersect.
2. Substitution: Solve one equation for one variable and substitute it into the other equation. For example, solve the first equation for x: x = y/2. Substitute this expression for x into the second equation: y = -(y/2)^2 + 4. Simplify and solve for y. Once you have the value(s) of y, substitute them back into the first equation to find the corresponding x-value(s).
3. Elimination: Multiply the first equation by 2 to make the coefficients of x in both equations the same. This gives us 2x = y. Substitute this expression for y in the second equation: y = -x^2 + 4. Simplify and solve for x. Once you have the value(s) of x, substitute them back into the first equation to find the corresponding y-value(s).
Note that the solutions to this equation may be real numbers, complex numbers, or a combination of both, depending on the specific values of x and y.
1. Graphing: Plot the graphs of y = 2x and y = -x^2 + 4. The solution(s) will be the x-coordinates of the points where the two graphs intersect.
2. Substitution: Solve one equation for one variable and substitute it into the other equation. For example, solve the first equation for x: x = y/2. Substitute this expression for x into the second equation: y = -(y/2)^2 + 4. Simplify and solve for y. Once you have the value(s) of y, substitute them back into the first equation to find the corresponding x-value(s).
3. Elimination: Multiply the first equation by 2 to make the coefficients of x in both equations the same. This gives us 2x = y. Substitute this expression for y in the second equation: y = -x^2 + 4. Simplify and solve for x. Once you have the value(s) of x, substitute them back into the first equation to find the corresponding y-value(s).
Note that the solutions to this equation may be real numbers, complex numbers, or a combination of both, depending on the specific values of x and y.
A triangle in which two altitudes of the triangle are two of its sides is _________.- a)obtuse-angled triangle
- b)acute-angled triangle
- c)right-angled triangle
- d)None of these
Correct answer is option 'C'. Can you explain this answer?
A triangle in which two altitudes of the triangle are two of its sides is _________.
a)
obtuse-angled triangle
b)
acute-angled triangle
c)
right-angled triangle
d)
None of these
|
Prisha Banerjee answered |
A right triangle (American English) or right-angled triangle (British English) is a triangle in which one angle is a right angle (that is, a 90-degree angle). The relation between the sides and angles of a right triangle is the basis for trigonometry.
The side opposite the right angle is called the hypotenuse (side c in the figure). The sides adjacent to the right angle are called legs (or catheti, singular: cathetus). Side a may be identified as the side adjacent to angle B and opposed to (or opposite) angle A, while side b is the side adjacent to angle A and opposed to angle B.
If the lengths of all three sides of a right triangle are integers, the triangle is said to be a Pythagorean triangle and its side lengths are collectively known as a Pythagorean triple.
Which is the longest side in the triangle PQR right angled at P?- a)PR
- b)PQ
- c)QR
- d)None of these
Correct answer is option 'C'. Can you explain this answer?
Which is the longest side in the triangle PQR right angled at P?
a)
PR
b)
PQ
c)
QR
d)
None of these
|
Rajat Singh answered |
The side opposite to greater angle is greater, and in a right angled triangle, the right angle is the largest angle. So side opposite to it is the largest and known as hypotenuse. In our question, since right angle is at P so the side opposite to it will be QR.
How many altitude can a triangle have?- a)2
- b)3
- c)1
- d)None of these
Correct answer is option 'B'. Can you explain this answer?
How many altitude can a triangle have?
a)
2
b)
3
c)
1
d)
None of these
|
|
Sania Arju answered |
Since all triangles have three vertices and three opposite sides, all triangles have three altitudes. The three altitudes of any triangle (or lines containing the altitudes) intersect at a common location called the orthocentre.
The orthocentre occurs inside a triangle if and only if the triangle is an acute triangle.
The orthocentre is coincidental with the vertex where the right angle occurs if and only if the triangle is a right triangle.
The orthocentre occurs outside a triangle if and only if the triangle is an obtuse triangle.
The orthocentre occurs inside a triangle if and only if the triangle is an acute triangle.
The orthocentre is coincidental with the vertex where the right angle occurs if and only if the triangle is a right triangle.
The orthocentre occurs outside a triangle if and only if the triangle is an obtuse triangle.
Which is the longest side of a right triangle?- a)Hypotenuse
- b)Base
- c)Perpendicular
- d)None of these
Correct answer is option 'A'. Can you explain this answer?
Which is the longest side of a right triangle?
a)
Hypotenuse
b)
Base
c)
Perpendicular
d)
None of these
|
Geeta Sharma answered |
A because if we draw right triangle neeche vala base 90 vala perpendicular remain hypotenuse so it is longest
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