Question

Corresponding sides of two similar triangles are in the ratio 2 : 3. If the area of the smaller triangle is 48 ${cm}^2$, determine the area of the larger triangle.

Answer 1

Given, ratio of corresponding sides of two similar triangles $=2:3$ or $\frac{2}{3}$

Area of smaller triangle $=48c{m}^2$

By the property of area of two similar triangle,

$Ratioofareaofbothtriangles=(Ratiooftheircorrespondingsides{)}^2$

$\Rightarrow$ $\frac{ar\left(smallertriangle\right)}{ar\left(largertriangle\right)}={\left(\frac{2}{3}\right)}^2$

$\Rightarrow$ $\frac{48}{ar\left(largertriangle\right)}=\frac{4}{9}$

$\Rightarrow$ Area of larger triangle $=\frac{48\times 9}{4}=12\times 9=108c{m}^2$