Question 11 Mark

In the following figure $\angle MNP=90^{\circ}$, $seg\ NQ \perp seg\ MP$, $MQ=9$, $QP=4$, find NQ.

Answer

In right-angled $\Delta MNP$, $seg\ NQ$ is the altitude to the hypotenuse.
By the Property of Geometric Mean:
$NQ^{2} = MQ \times QP$
$NQ^{2} = 9 \times 4 = 36$
$NQ = \sqrt{36} = 6$

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