Question

*In the given figure, QN is perpendicular to PR, Find QN.*

1️⃣ 12
2️⃣ 14
3️⃣ 16
4️⃣ 9​

Answer 1

Answer:

option 1 is correct

Step-by-step explanation:

By geometric mean

PN ×NR=QN²

∴9×16=144

∴QN²=144

squaring both the sides, we get

QN=12

Answer 2

Given : QN is perpendicular to PR

To Find :  QN.

1️⃣ 12

2️⃣ 14

3️⃣ 16

4️⃣ 9​

Step-by-step explanation:

Compare Δ QNR and ΔPNQ

∠QNR =  ∠PNQ = 90°

∠R  =  ∠NQP   = (90° - P )

∠RQN  = ∠P    =  (90° - R )

Δ QNR ≈ ΔPNQ

=> QN/PN  = NR/QN

=> QN² = PN x NR

=> QN² = 9 x 16

=> QN² = 3² x  4²

=> QN = 3 x 4

=> QN =12

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