Q3 of 45 Page 38

In figure 2.18, ∠QPR = 90°, seg PM ⊥ seg QR and Q – M – R,PM = 10, QM = 8, find QR.

In ∆PMQ, ∠PMQ = 900


So PM2 + QM2 = PQ2


PQ2 = 164 …(1)


In ∆PQR, ∠RPQ = 900


So PQ2 + PR2 = QR2


⇒ 164 + PR2 = QR2


⇒ PR2 = QR2 – 164 …(2)


In ∆PMR, ∠PMR = 900


So PM2 + MR2 = PR2


⇒ 100 + (QR – QM)2 = QR2 – 164


⇒ 100 + QR2 – 2.QR.QM + QM2 = QR2 – 164


⇒ 100 – 2.QR.8 + 64 = – 164


⇒ 16QR = 2×164


⇒ QR = 20.5


Thus QR = 20.5


More from this chapter

All 45 →
1

Identify, with reason, which of the following are Pythagorean triplets.

(i) (3, 5, 4) (ii) (4, 9, 12)


(iii) (5, 12, 13) (iv) (24, 70, 74)


(v) (10, 24, 27) (vi) (11, 60, 61)

 2

In figure 2.17, ∠MNP = 90°, seg NQ ⊥ seg MP, MQ = 9,QP = 4, find NQ.

 4

See figure 2.19. Find RP and PSusing the information given in ΔPSR.


Ans. RP = 12, PS = 6

 5

For finding AB and BC with the help of information given in figure 2.20, complete following activity.