Question

In the figure 2.22, M is the midpoint of QR. ∠PRQ = 90°. Prove that, PQ²=4PM²-3PR²

Answer 1

Given :

In ∆PRQ , <PRQ = 90° ,

M is the midpoint of QR .

To prove :

PQ² = 4PM² - 3PR²

Proof :

In right triangles PQR and PMR ,

we have

PQ² = PR² + QR² ----( 1 )

PM² = PR² + RM² --- ( 2 )

Now ,

PQ² = PR² + QR²

=> PQ² = PR² + 4RM²

[ Since , RM = QM = QR/2 ]

=>PQ² =PR² + 4( PM² - PR² ) [ from(2)]

=> PQ² = PR² + 4PM² - 4PR²

=> PQ² = 4PM² - 3PR²

Answer 2

HOPE IT HELPS YOU!!!