Corresponding sides of two similar triangles are in the ratio of 2 : 3. If the area of the smaller triangle is 48 cm², find the area of the larger triangle
Solution:
Given, the ratio of corresponding sides of two similar triangles = 2:3
Area of the smaller triangle = 48 square cm.
We have to find the area of the larger triangle.
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 smaller triangle/area of larger triangle = (2/3)²
48/area of larger triangle = 4/9
48(9) = 4(area of larger triangle)
12(9) = area of larger triangle.
Area of larger triangle = 108 square cm.
Therefore, the area of the larger triangle is 108 square cm.
✦ Try This: Corresponding sides of two similar triangles are in the ratio of 3:4. If the area of the smaller triangle is 15 square cm, find the area of the larger triangle.
Given, the ratio of corresponding sides of two similar triangles = 3:4
Area of the smaller triangle = 15 square cm.
We have to find the area of the larger triangle.
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 smaller triangle/area of larger triangle = (3/4)²
15/area of larger triangle = 9/16
15(16) = 9(area of larger triangle)
5(16) = 3(area of larger triangle)
Area of larger triangle = 80/3 = 26.67 square cm
Therefore, the area of the larger triangle is 26.67 square cm
☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 6
NCERT Exemplar Class 10 Maths Exercise 6.3 Problem 10
Corresponding sides of two similar triangles are in the ratio of 2 : 3. If the area of the smaller triangle is 48 cm², find the area of the larger triangle
Summary:
Corresponding sides of two similar triangles are in the ratio of 2 : 3. If the area of the smaller triangle is 48 square cm, the area of the larger triangle is 26.67 square cm
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