Question

The corresponding sides of two similar triangles are in the ratio of $2:3$. If the area of the smaller triangle is $48c{m}^2$, find the area of the larger triangle.

Answer 1

Given:

The ratio of two similar triangles is $2:3$.

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

Let area of larger triangle be $x$.

If two triangles are similar, then the ratio of their areas is equal to the ratio of the squares of their corresponding sides.

$\Rightarrow \frac{48}{x}=\frac{2^2}{3^2}$

$\Rightarrow \frac{48}{x}=\frac{4}{9}$

$\Rightarrow \frac{x}{48}=\frac{9}{4}$

$\Rightarrow x=\frac{9}{4}\times 48$

$\Rightarrow x=9\times 12$

$\Rightarrow x=108$

Therefore, Area of larger triangle is $108c{m}^2$.