Question

Corresponding sides of two similar triangles are in the ratio $2:1$. If the area of the smaller triangle is $48c{m}^2$, find the area of the larger triangle.

Answer 1

Step 1: Finding the area of the larger triangle

Given that ratio of corresponding sides of similar triangles is $2:1$

The area of the smaller triangle $=48c{m}^2$

Similar Triangles property: The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides.

$\therefore \frac{Areaoflargertriangle}{Areaofsmallertriangle}={\left(\frac{2}{1}\right)}^2$

Let $xc{m}^2$ be the area of the larger triangle.

$\Rightarrow \frac{x}{48}=\frac{4}{1}$

$\Rightarrow x=4\times 48$

$\Rightarrow x=192c{m}^2$

Hence, the area of the larger triangle is $192c{m}^2$.