Question

In $△ABC$ and $△PQR$, $\angle A=\angle R,\angle B=\angle Q,AB=28,BC=10,AC=24,PQ=5$ and $QR=14$. Then the length of the side $PR$ is :

• A. $10$
• B. $12$
• C. $20$
• D. $26$

Answer 1

The correct option is B $12$

Considering the triangles $\Delta ABC$ and $\Delta PQR$

$\angle A=\angle R$ ....Given

$\angle B=\angle Q$. Given

If two of their angles are equal, then the third angle must also be equal, because angles of a triangle always add to make 180

$\Rightarrow \angle C=\angle P$

So, by $AAA$ similarity

$\Delta ABC$ $\sim$ $\Delta RQP$

the lengths of the corresponding sides of two similar triangles are proportional.

$\Rightarrow \frac{AB}{QR}=\frac{AC}{PR}=\frac{BC}{PQ}$

$\frac{AC}{PR}=\frac{BC}{PQ}$

$\Rightarrow \frac{24}{PR}=\frac{10}{5}$

$\Rightarrow PR=12$