Question

Two triangles are similar and ratio of their corresponding side is $2:5$. If the area of the smaller triangle is $64{\text{cm}}^2$, find the area of the larger triangle.

Answer 1

Finding the area of larger triangle:

We know that the ratio of area of two similar triangles is equal to the squares of the ratio of corresponding sides.

therefore we have, $\frac{ar(\text{Small}△)}{ar(\text{Large}△)}=$Square of Ratio of the corresponding sides.

Given the ratio of corresponding sides = $2:5$

Therefore $\frac{ar(\text{Small}△)}{ar(\text{Large}△)}={\left(\frac{2}{5}\right)}^2$

$\Rightarrow \frac{64}{ar(\text{Large}△)}=\frac{4}{25}$

$$\begin{gathered} \Rightarrow ar(\text{Large}△)=64\times \frac{25}{4} \\ \Rightarrow ar(\text{Large}△)=400{\text{cm}}^2 \end{gathered}$$

Thus the area of the larger triangle is $400{\text{cm}}^2$.