Question

In triangle PRQ. angle PRQ = 90°. Then prove that, PQ²=4PM²-3PR².​

Answer 1

Answer:

To prove : PQ

2

=4PM

2

−3PR

2

Proof :-

In ΔPRM

PM

2

=PR

2

+RM

2

(Pythagoras theorem) ⟶(1)

Also,

In ΔPQR

PQ

2

=PR

2

+RQ

2

=PR

2

+(RM+MQ)

2

=PR

2

+(RM+RM)

2

(∵RM=MQ)

=PR

2

+4RM

2

⟶(2)

From (1),

RM

2

=PM

2

−PR

2

⟶(3)

Putting (3) in (2) we get

PQ

2

=PR

2

+4(PM

2

−PR

2

)

PQ

2

=PR

2

+4PM

2

−4PR

2

PQ

2

=4PM

2

−3PR

2