Question

angle PQR=90°,QN perpendicular PR PN=9, NR=16.Find QN.​

Answer 1

Given:

∠PQR = 90°

QN ⊥ PR

PN = 9, NR = 16

To Find

QN

Solution:

 In ΔPQR,

   Segment QN is perpendicular to PR (given)

        NQ² = PN × NR                     [ theorem of geometric mean]

        NQ = $\sqrt{PN * NR}$

                = $\sqrt{9 * 16}$

                = 3 × 4

                = 12

              QN = 12

Therefore, the value of QN is 12.

           

         

Answer 2

we know that in right angle triangle the perpendicular segment to the hypotenuse from the opposite vertex is the geometric mean of the segments into which the hypotenuse is divided here is mint pm perpendicular segment QR

pn ²=qm×mr

10²=8×mr

mr=100/8

mr=25/2

now

qr=qm+mr

=8+25/2

=20.5