Question:
Corresponding sides of two triangles are in the ratio $2: 3 .$ If the area of the smaller triangle is $48 \mathrm{~cm}^{2}$, determine the area of the larger triangle.
Solution:
The ratio of the areas of two similar triangles is equal to the ratio of the square of any two corresponding sides.
$\frac{\text { Area of triangle }}{\text { Area of larger triangle }}=\frac{(\text { Corresponding side of smaller triangle })^{2}}{(\text { Corresponding side of larger triangle })^{2}}$
$\frac{\text { Area of triangle }}{\text { Area of larger triangle }}=\frac{2^{2}}{3^{2}}$
$\frac{48}{\text { Area of larger triangle }}=\frac{4}{9}$
Area of larger triangle $=\frac{48 \times 9}{4}$
Area of larger triangle $=108$
Hence the area of the larger triangle is