Question

The perimeter of two similar triangles $△ABC$ and $△DEF$ are $36$ cm and $24$ cm respectively. If $DE=10$ cm, then $AB$ is :

• A. $12$ cm
• B. $20$ cm
• C. $15$ cm
• D. $18$ cm

Answer 1

Answer: (C)

$15$ cm

Given that triangles $ABC$ and $DEF$ are similar.

Also given, $DE=10$ cm and perimeters of triangles $ABC$ and $DEF$ are $36$ cm and $24$ cm.

So, the corresponding sides of the two triangles is equal to the ratio of their perimeters.

Hence, $\frac{\text{perimeter of}ABC}{\text{perimeter of}DEF}$ $=\frac{AB}{DE}$

Therefore, $\frac{36}{24}=\frac{AB}{10}$

$\Rightarrow AB=\frac{36\times 10}{24}$

$\Rightarrow AB=15$ cm