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Three villages P, Q, and R are located in such a way that the distance PQ = 13 km, QR = 14 km, and RP = 15 km, as shown in the figure. A straight road joins Q and R. It is proposed to connect P to this road QR by constructing another road. What is the minimum possible length (in km) of this connecting road? Note: The figure shown is representative.
- 10.5
- 11.0
- 12.0
- 12.5
Correct answer: 12.0
Solution
Triangle sides 13,14,15: Heron area = sqrt(21*8*7*6)=84. Altitude to QR (=14) is 2*84/14=12 km. The minimum connecting road is 12.0 km, not 12.5.
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