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Altitude and base of a right angle triangle are (x + 2) and (2x + 3) (in cm). If the area of the triangle be 60 , the length of the hypotenuse is :
- a)21 cm
- b)13 cm
- c)17 cm
- d)15 cm
- e)None of these
Correct answer is option 'C'. Can you explain this answer?
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Altitude and base of a right angle triangle are (x + 2) and (2x + 3) (...
Option C
2x2 + 7x-114 =n 0
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Altitude and base of a right angle triangle are (x + 2) and (2x + 3) (...
Given that the altitude (height) of the right angle triangle is (x + 2) cm and the base is (2x + 3) cm, we can find the length of the hypotenuse using the Pythagorean theorem.
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
Let's assume the hypotenuse is h cm.
We can write the equation as:
h^2 = (x + 2)^2 + (2x + 3)^2
To find the value of x, we need to solve the equation for x.
Expanding the equation:
h^2 = x^2 + 4x + 4 + 4x^2 + 12x + 9
Combining like terms:
h^2 = 5x^2 + 16x + 13
Since the area of the triangle is given as 60 cm^2, we can use the formula for the area of a right triangle to get another equation.
The formula for the area of a right triangle is:
Area = (base * height) / 2
Substituting the given values:
60 = [(2x + 3) * (x + 2)] / 2
120 = (2x + 3) * (x + 2)
120 = 2x^2 + 7x + 6
Now we have a system of equations:
Equation 1: h^2 = 5x^2 + 16x + 13
Equation 2: 120 = 2x^2 + 7x + 6
We can solve this system of equations to find the value of x. Once we have the value of x, we can substitute it back into either equation to find the length of the hypotenuse (h).
Solving the system of equations, we find x = 2.
Now we can substitute x = 2 into Equation 1 to find the length of the hypotenuse:
h^2 = 5(2)^2 + 16(2) + 13
h^2 = 20 + 32 + 13
h^2 = 65
h = √65
Therefore, the length of the hypotenuse is √65 cm, which is approximately 8.06 cm.
Since none of the given options match the calculated length of the hypotenuse, the correct answer would be None of these.
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
Let's assume the hypotenuse is h cm.
We can write the equation as:
h^2 = (x + 2)^2 + (2x + 3)^2
To find the value of x, we need to solve the equation for x.
Expanding the equation:
h^2 = x^2 + 4x + 4 + 4x^2 + 12x + 9
Combining like terms:
h^2 = 5x^2 + 16x + 13
Since the area of the triangle is given as 60 cm^2, we can use the formula for the area of a right triangle to get another equation.
The formula for the area of a right triangle is:
Area = (base * height) / 2
Substituting the given values:
60 = [(2x + 3) * (x + 2)] / 2
120 = (2x + 3) * (x + 2)
120 = 2x^2 + 7x + 6
Now we have a system of equations:
Equation 1: h^2 = 5x^2 + 16x + 13
Equation 2: 120 = 2x^2 + 7x + 6
We can solve this system of equations to find the value of x. Once we have the value of x, we can substitute it back into either equation to find the length of the hypotenuse (h).
Solving the system of equations, we find x = 2.
Now we can substitute x = 2 into Equation 1 to find the length of the hypotenuse:
h^2 = 5(2)^2 + 16(2) + 13
h^2 = 20 + 32 + 13
h^2 = 65
h = √65
Therefore, the length of the hypotenuse is √65 cm, which is approximately 8.06 cm.
Since none of the given options match the calculated length of the hypotenuse, the correct answer would be None of these.
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Altitude and base of a right angle triangle are (x + 2) and (2x + 3) (in cm). If the area of the triangle be 60 , the length of the hypotenuse is :a)21 cmb)13 cmc)17 cmd)15 cme)None of theseCorrect answer is option 'C'. Can you explain this answer?
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