Question

Find the length of PQ (in m) from the given figure:

• A. 25

Answer 1

The correct option is A 25
We know, if any two right triangles have an acute angle measure in common, then the ratios of their corresponding side lengths in the two triangles would be equal.



In ΔMNO and ΔMPQ:

$\angle MNO=\angle MPQ\left(\text{Each}{90}^{\circ }\right)$

$\angle NMO=\angle PMQ\text{(Common)}$

$\text{Therefore,}\frac{MQ}{MO}=\frac{PQ}{NO}$

$\Rightarrow \frac{25}{55}=\frac{PQ}{55}$

$\Rightarrow \frac{5}{11}\times 55=PQ$

$\Rightarrow 25=PQ$

Therefore, the length of PQ is 25 m.