# Corresponding sides of two similar triangles are in the ratio 1 : 3.

Question:

Corresponding sides of two similar triangles are in the ratio $1: 3$. If the area of the smaller triangle in $40 \mathrm{~cm}^{2}$, find the area of the larger triangle.

Solution:

Since the ratio of areas of two similar triangles is equal to the ratio of the squares of any two corresponding sides.

$\frac{\text { Area of smaller triangle }}{\text { Area of larger triangle }}=\frac{\text { (Corresponding side of smaller triangle) }^{2}}{\text { (Corresponding side of larger triangle) }^{2}}$

$\frac{\text { Area of smaller triangle }}{\text { Area of larger triangle }}=\frac{1^{2}}{3^{2}}$

$\frac{40}{\text { Area of larger triangle }}=\frac{1}{9}$

Area of larger triangle $=\frac{40 \times 9}{1}=360 \mathrm{~cm}^{2}$

Hence the area of the larger triangle is $360 \mathrm{~cm}^{2}$