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Question
In the given figure, ∠MNP = 90°, seg NQ ⊥ seg MP, MQ = 9, QP = 4, find NQ.
Sum
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Solution
Given: In ∆MNP,
∠MNP = 90°
NQ ⊥ MP
MQ = 9,
QP = 4
We know that.
In a right-angled triangle, the perpendicular segment to the hypotenuse from the opposite vertex is the geometric mean of the segments into which the hypotenuse is divided.
∴ NQ2 = MQ × QP ...[Theorem of geometric mean]
∴ NQ2 = 9 × 4
∴ NQ2 = 36
∴ NQ = 6 ...[Taking square root on both side]
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Theorem of Geometric Mean
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