Question

The corresponding sides of two similar triangles are in the ratio 2 : 3. If the area of the smaller triangle is 48 cm², find the area of the larger triangle.

Answer 1

Given, ratio of corresponding sides of two similar triangles = 2 : 3 or `2/3`

Area of smaller triangle = 48 cm²

By the property of area of two similar triangle,

Ratio of area of both triangles = (Ratio of their corresponding sides)² 

i.e., `("ar(smaller triangle)")/("ar(larger triangle)") = (2/3)^2`

⇒ `48/("ar(larger triangle)") = 4/9`

⇒ ar(larger triangle) = `(48 xx 9)/4`

= 12 × 9

= 108 cm²