Quantitative Aptitude – Geometry – Triangles – A triangle ABC has area 32 sq units

Slot -2 – Quantitative Aptitude – Geometry – Triangles – A triangle ABC has area 32 sq units

A triangle ABC has area 32 sq units and its side BC, of length 8 units, lies on the line x = 4. Then the shortest possible distance between A and the point (0,0) is?

a) 4√2 units
b) 8 units
c) 4 units
d) 2√2 units

Answer: c) 4 units

Solution: The distance OA will be minimum when the perpendicular from A on BC will pass through O.

Area of triangle ABC = 1/2 BC×AD = 1/2×8×(AO+OD ) = 4×(AO+4)
32 = 4AO+16
AO = 4
So required minimum distance = 4

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