Question

The perimeters of two similar triangles, $△ABC$ and $△PQR$ are respectively $36$ cm and $24$ cm. If $PQ=10$ cm, then $AB$ is:

• A. $10$ cm
• B. $20$ cm
• C. $25$ cm
• D. $15$ cm

Answer 1

The correct option is D $15$ cm

$△ABC$ and $△$ PQR are similar.
Therefore, their respective sides and perimeters are also in proportion.
Given--- Perimeter of $△ABC=36$ cm
Perimeter of $△PQR=24$ cm

Therefore, their ratio is $\frac{36}{24}=\frac{3}{2}$.

Now, because $△ABC$ and $△PQR$ are similar.

$\therefore \frac{AB}{PQ}=\frac{3}{2}$

Given $PQ=10$ cm

$\therefore \frac{AB}{10}=\frac{3}{2}$

$\therefore AB=15$ cm