Question

In the given figure, ∠MNP = 90°, seg NQ ⊥ seg MP, MQ = 9, QP = 4, find NQ.

Answer 1

In ∆MNP,

`{:(∠"MNP" = 90°), ("seg NQ ⊥ seg MP"), ("MQ = 9, QP = 4"):}   }"Given"`

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]

∴ NQ = `sqrt("MQ" × "QP")` ...[Taking square root of both sides]

∴ NQ = `sqrt(9 × 4)`

∴ NQ = `sqrt(36)`

∴ NQ = 6