Question

please answer this question..​

Answer 1

Step-by-step explanation:

Given in right triangle PQR, QS = SR

By Pythagoras theorem,

we have PR2 = PQ2 + QR2 → (1)

In right triangle PQS,

we have PS2 = PQ2 + QS2

= PQ2 + (QR/2)2 [Since QS = SR = 1/2 (QR)]

= PQ2 + (QR2/4) 4PS2

= 4PQ2 + QR2

∴ QR2 = 4PS2 − 4PQ2 → (2)

Put (2) in (1),

we get PR2 = PQ2 + (4PS2 − 4PQ2)

∴ PR2 = 4PS2 − 3PQ2