Q2 of 45 Page 38

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

In ∆MNP, ∠ MNP = 900,


MN2 + NP2 = MP2


⇒ MN2 + NP2 = (MQ + QP)2


⇒ MN2 + NP2 = (13)2


⇒ MN2 + NP2 = 169 … (1)


In ∆MQN, ∠MQN = 900,


QN2 + MQ2 = MN2


⇒ QN2 + 92 = MN2


⇒ QN2 + 81 = MN2 …(2)


In ∆PQN, ∠PQN = 900,


QN2 + PQ2 = PN2


⇒ QN2 + 42 = PN2


⇒ QN2 + 16 = PN2 … (3)


Now (2) + (3)


⇒ QN2 + 81 + QN2 + 16 = MN2 + PN2


⇒ 2QN2 + 97 = 169 [from(1)]


⇒ 2QN2 = 72


⇒ QN2 = 36


Thus NQ = 6.


More from this chapter

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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)

 3

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

 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.