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Two upright poles AP and BQ stand at points A and B respectively. If AP = 16 m, BQ = 22 m, and the distance AB = 20 m, then for a point R on AB, the value of AR for which RP² + RQ² is least is

1. 5 m
2. 6 m
3. 10 m
4. 14 m

Correct answer: 10 m

Solution

Let AR=t, RB=20-t. RP^2+RQ^2=(t^2+16^2)+((20-t)^2+22^2)=2t^2-40t+1140. Minimum at t=40/4=10 m. So AR=10 m.

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