Question

In the given figure, the value of $x$ (in cm) is :

• A. 4
• B. 5
• C. 6
• D. 8

Answer 1

Answer: (B)

In $△APB\text{and}△QPR$,

$\frac{PA}{PQ}=\frac{2.4}{6}=\frac{2}{5}$

$\frac{PB}{PR}=\frac{3.2}{8}=\frac{2}{5}$

$\Rightarrow \frac{PA}{PQ}=\frac{PB}{PR}$

and $\angle APB=\angle QPR$

So, By SAS Similarity,

$△APB\sim △QPR$

$\Rightarrow \frac{PA}{PQ}=\frac{AB}{QR}$

$\Rightarrow \frac{2}{5}=\frac{2}{x}$

$\Rightarrow x=\frac{2\times 5}{2}$

$\Rightarrow x=5cm$

Hence, Option B is correct.