Question

Question 10
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, the ratio of corresponding sides of two similar triangles = 2 : 3
Area of smaller triangle = $48c{m}^2$

By the property of area of two similar triangles,
$Ratioofareasofbothtriangles=(Ratiooftheircorrespondingsides{)}^2$
$i.e.,\frac{ar\left(smallertraingle\right)}{ar\left(largertriangle\right)}={\left(\frac{2}{3}\right)}^2$

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

$\Rightarrow ar\left(largertriangle\right)=\frac{48\times 9}{4}=12\times 9=108c{m}^2$

Therefore, the area of larger triangle = $108c{m}^2$