Question

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

• A. 48 cm
• B. 36 cm
• C. 24 cm
• D. 12 cm

Answer 1

The correct option is A 48 cm

Let’s assume the triangle similar to $\Delta \text{ABC}$ to be $\Delta \text{XYZ}$. The ratio of corresponding sides is 2.
So, $\frac{XY}{AB}=\frac{YZ}{BC}=\frac{XZ}{AC}=2$ (Since it is asked for larger triangle)
$\Rightarrow \frac{XY}{6}=\frac{YZ}{8}=\frac{XZ}{10}=2$
$\Rightarrow$ XY = 12 cm, YZ = 16 cm and XZ = 20 cm.
The perimeter of $\Delta \text{XYZ}$ is XY + YZ + XZ = 12 + 16 + 20 = 48 cm.