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

Given: The ratio of corresponding sides is 2.

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

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

$\frac{\text{Perimeter of}(\Delta \text{XYZ)}}{\text{Perimeter of}\left(\Delta \text{ABC}\right)}=2$..........(Ratio of perimeters of similar triangles)

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

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