Question

In the given figure, ∠PQR = 90 degrees

and QM ⊥ PR. If QM = 10 cm, PM = 5

cm then find RM.

Answer 1

In △PQR,m∠Q=90

o

and

QM

is an altitude; M∈

PR

∴ P−M−R, QM

2

=PM.MR

Suppose PM=a

∴ RM=PR−PM=26−a

Now, QM

2

=PM.RM

⇒ 12

2

=a(26−a)

⇒ 144=26a−a

2

⇒ a

2

−26a+144=0

⇒ (a−8)(a−18)=0

⇒ a=8 or a=18

So PM=8 and RM=18 or

PM=18 and RM=8

If PM<RM, then PM=8 and RM=18

PQ

2

=PM.PR=8×26=16×13

⇒ PQ=4

13

QR

2

=RM.PR=18×26=36×13

QR=6

13