GATE 2025 ST – Question 10

General Aptitude · Quantitative Aptitude: Algebra, Geometry and Mensuration · 2 marks · Multiple choice

Villages P,Q,R have PQ=13 km,QR=14 km,RP=15 km as shown. A straight road joins Q,R. Find the minimum length of a road connecting P to road QR (km).

10.5
11.0
12.0
12.5

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Show answer and explanation

Correct answer: (C) 12.0

Explanation

The shortest connector is the perpendicular altitude. Heron’s formula gives semiperimeter 21 and area √(21·8·7·6)=84 km². Altitude=2×84/14=**12 km, C**. Its foot lies on QR because the projection distance from Q is (13²+14²−15²)/(2·14)=5 km.

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