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The lengths of a triangle are 6 cm, 8 cm and 10 cm. Then the length of perpendicular from the opposite vertex to the side whose length is 8cm is:
- a)5 cm
- b)4 cm
- c)6 cm
- d)2 cm
Correct answer is option 'C'. Can you explain this answer?
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The lengths of a triangle are 6 cm, 8 cm and 10 cm. Then the length of...
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The lengths of a triangle are 6 cm, 8 cm and 10 cm. Then the length of...
It is a right triangle in which 8cm is base , 6cm is height and 10cm is hypotenuse.
so , 6cm is perpendicular to 8cm
so , 6cm is perpendicular to 8cm
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The lengths of a triangle are 6 cm, 8 cm and 10 cm. Then the length of...
Given:
The lengths of a triangle are 6 cm, 8 cm, and 10 cm.
To find:
The length of the perpendicular from the opposite vertex to the side whose length is 8 cm.
Solution:
We have a triangle with side lengths 6 cm, 8 cm, and 10 cm. Let's label the vertices as A, B, and C, and the sides opposite to these vertices as a, b, and c respectively.
Step 1: Verify Triangle Inequality Theorem
According to the Triangle Inequality Theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
Let's verify this for the given triangle:
- Side a + Side b > Side c
- 6 cm + 8 cm > 10 cm
- 14 cm > 10 cm (True)
- Side b + Side c > Side a
- 8 cm + 10 cm > 6 cm
- 18 cm > 6 cm (True)
- Side c + Side a > Side b
- 10 cm + 6 cm > 8 cm
- 16 cm > 8 cm (True)
Since all the inequalities hold true, the given side lengths form a valid triangle.
Step 2: Identify the Required Perpendicular
We need to find the length of the perpendicular from the vertex opposite to the side of length 8 cm (vertex C) to the side of length 8 cm (side AB).
Step 3: Draw the Perpendicular
Draw a perpendicular from vertex C to side AB. Let's label the point of intersection as D.
Step 4: Identify the Right Triangle
In triangle ABC, the perpendicular from vertex C to side AB creates a right triangle. Let's label the right triangle as ADC.
Step 5: Apply Pythagoras Theorem
In the right triangle ADC, we can apply the Pythagoras theorem to find the length of the perpendicular AD.
The Pythagoras theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
In triangle ADC:
AC² = AD² + CD²
We know that AC is the side of length 10 cm, and CD is the side of length 8 cm.
Using the Pythagorean theorem:
10² = AD² + 8²
100 = AD² + 64
AD² = 100 - 64
AD² = 36
AD = √36
AD = 6 cm
Therefore, the length of the perpendicular from vertex C to side AB is 6 cm.
Hence, the correct answer is option C) 6 cm.
The lengths of a triangle are 6 cm, 8 cm, and 10 cm.
To find:
The length of the perpendicular from the opposite vertex to the side whose length is 8 cm.
Solution:
We have a triangle with side lengths 6 cm, 8 cm, and 10 cm. Let's label the vertices as A, B, and C, and the sides opposite to these vertices as a, b, and c respectively.
Step 1: Verify Triangle Inequality Theorem
According to the Triangle Inequality Theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
Let's verify this for the given triangle:
- Side a + Side b > Side c
- 6 cm + 8 cm > 10 cm
- 14 cm > 10 cm (True)
- Side b + Side c > Side a
- 8 cm + 10 cm > 6 cm
- 18 cm > 6 cm (True)
- Side c + Side a > Side b
- 10 cm + 6 cm > 8 cm
- 16 cm > 8 cm (True)
Since all the inequalities hold true, the given side lengths form a valid triangle.
Step 2: Identify the Required Perpendicular
We need to find the length of the perpendicular from the vertex opposite to the side of length 8 cm (vertex C) to the side of length 8 cm (side AB).
Step 3: Draw the Perpendicular
Draw a perpendicular from vertex C to side AB. Let's label the point of intersection as D.
Step 4: Identify the Right Triangle
In triangle ABC, the perpendicular from vertex C to side AB creates a right triangle. Let's label the right triangle as ADC.
Step 5: Apply Pythagoras Theorem
In the right triangle ADC, we can apply the Pythagoras theorem to find the length of the perpendicular AD.
The Pythagoras theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
In triangle ADC:
AC² = AD² + CD²
We know that AC is the side of length 10 cm, and CD is the side of length 8 cm.
Using the Pythagorean theorem:
10² = AD² + 8²
100 = AD² + 64
AD² = 100 - 64
AD² = 36
AD = √36
AD = 6 cm
Therefore, the length of the perpendicular from vertex C to side AB is 6 cm.
Hence, the correct answer is option C) 6 cm.
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Solutions for The lengths of a triangle are 6 cm, 8 cm and 10 cm. Then the length of perpendicular from the opposite vertex to the side whose length is 8cm is:a)5 cmb)4 cmc)6 cmd)2 cmCorrect answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for Class 9.
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