Question

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.

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