Question

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

Answer 1

Given, ratio of corresponding sides of two similar triangles = 2 : 3 or $\frac{2}{3}$
Area if similar triangle = $45c{m}^2$
By the property of area of two similar triangle,
Ratio of area of both triangles = $(Ratiooftheircorrespondingsides{)}^2$
i.e., $\frac{ar\left(smallertraingel\right)}{ar\left(largertriangle\right)}={\left(\frac{2}{3}\right)}^2$
$\Rightarrow \frac{48}{ar\left(largertriangle\right)}=\frac{4}{9}$ $\Rightarrow ar\left(largertriangle\right)=\frac{48\times 9}{4}=12\times 9=108c{m}^2$