Question

The sides of $\Delta \text{ABC}$ are 6 cm, 8 cm and 10 cm. Find the perimeter of the larger $\Delta \text{XYZ}$ (in cm) which is similar to $\Delta \text{ABC}$ if the ratio of corresponding sides is 2 : 1.

• A. 48

Answer 1

The correct option is A 48

Let $\Delta \text{XYZ}$ be the larger triangle, similar to $\Delta \text{ABC}$.

Given, the ratio of corresponding sides is 2 : 1.

Since ratio of their corresponding sides is 2 : 1, the ratio of their perimeter will also be 2 : 1.

Perimeter of $\Delta \text{ABC}$$=6+8+10=24cm$

$\frac{\text{Perimeter of}\Delta \text{XYZ}}{\text{Perimeter of}\Delta \text{ABC}}=\frac{2}{1}$

$\frac{\text{Perimeter of}\Delta \text{XYZ}}{24}=2$

The perimeter of $\Delta \text{XYZ}=24\times 2=48\text{cm}$