Question

Find the length of PQ (in yd) in 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 In ΔMNO and ΔMPQ:

$\angle MNO=\angle MPQ\text{Each}{90}^{\circ }$

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

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

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

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

$\Rightarrow 25=PQ$

Therefore, the length of PQ is 25 yd.