Question

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

ar(smaller tri)/ar(larger tri)=one side square/one side square. so 48/x=(2)2/(3^3)so x=9/4^48=108

Answer 2

$\bf\huge\underline{Question}$

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.

$\bf\huge\underline{Solution}$

Given, ratio of corresponding sides of two similar traingles is 2 : 3 or $\dfrac{2}{3}$

Area of smaller traingle = 48 cm²

By the property of area of two similar traingles,

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

i.e., $\bf\dfrac{ar(smaller\:traingle)}{ar(larger traingle)}$ = ($\dfrac{2}{3}$)²

=> $\bf\dfrac{48}{ar(larger\:traingle)}$ = $\dfrac{4}{9}$

=> ar(larger traingle) = $\dfrac{48 × 9}{4}$

=> 12 × 9 = 108 cm²