Question

PQR is a right angle triangle right angled at Q, PR =41, PQ-QR=31 find PQ,QR

Answer 1

Answer:

Step-by-step explanation:

PQ-QR = 31 --------------------(1)

By Pythagoras theorem

PR² = PQ² + QR²

41² =  PQ² + QR² ---------------(2)

(PQ-QR)² = PQ² + QR² - 2×PQ×QR

31² = 41² - 2×PQ×QR

2×PQ×QR = 41² - 31² = 720

PQ×QR = 360 ------------(3)

From (1) , (2) and (3)

Substitute QR = 360/PQ  in (1)

PQ - 360/PQ = 31

PQ² - 360 = 31PQ

PQ² - 31PQ - 360 = 0

PQ² - 40PQ + 9PQ - 360 = 0

PQ(PQ-40) +9 (PQ-40) = 0

(PQ+9)(PQ-40) = 0

So PQ = 40

Substitute PQ = 40 in (1)

40 - QR = 31

QR = 9