Question

2. In APQR, 2Q = 90° and QD is an altitude. If PD = 9DR then PQ=_xQR
(a) 9
(b) 3
(c) 6
(d) 81​

Answer 1

Step-by-step explanation:

It is given that ∠PQR=90

0

, QS⊥PR, PD=4DR

Consider,

PQ

2

=PR×PD

PR=

PD

PQ

2

.......(1)

Similarly, we have,

QR

2

=PR×RD

PR=

RD

QR

2

.......(2)

Comparing equations 1 and 2 as follows:

PD

PQ

2

=

RD

QR

2

⇒

4DR

PQ

2

=

RD

QR

2

⇒

4

PQ

2

=QR

2

⇒PQ

2

=4QR

2

⇒

PQ

2

=

4QR

2

⇒PQ=2QR

Hence, PQ=2QR.

Hope it HELPS you