Areas of two similar triangles are 36 cm² and 100 cm² . If the length of a side of the larger triangle is 20 cm, find the length of the corresponding side of the smaller triangle
Solution:
Given, area of two similar triangles are 36cm² and 100cm²
The length of a side of the larger triangle is 20 cm
We have to find the corresponding side of the smaller triangle.
Let the corresponding side of the smaller triangle be x.
Area of the larger triangle be 100cm²
Area of the smaller triangle be 36cm²
We know that the ratio of the areas of two similar triangles is equal to the ratio of the squares of their corresponding sides.
So, area of larger triangle/area of smaller triangle = (side of larger triangle)²/(side of smaller triangle)²
100/36 = (20)²/x²
Taking square root,
10/6 = 20/x
On cross multiplication,
10x = 6(20)
10x = 120
x = 120/10
x = 12 cm
Therefore, the corresponding side of the smaller triangle is 12 cm.
✦ Try This: Areas of two similar triangles are 64 cm² and 169 cm². If the length of a side of the larger triangle is 18 cm, find the length of the corresponding side of the smaller triangle
☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 6
NCERT Exemplar Class 10 Maths Exercise 6.3 Problem 12
Areas of two similar triangles are 36 cm² and 100 cm². If the length of a side of the larger triangle is 20 cm, find the length of the corresponding side of the smaller triangle
Summary:
Areas of two similar triangles are 36 cm² and 100 cm². If the length of a side of the larger triangle is 20 cm, the length of the corresponding side of the smaller triangle is 12 cm
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