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Question

Mathematics Question on Coordinate Geometry

Let R be the point (3, 7) and let P and Q be two points on the line x + y = 5 such that PQR is an equilateral triangle, Then the area of ΔPQR is

A

2543\frac{25}{4\sqrt3}

B

2532\frac{25\sqrt3}{2}

C

253\frac{25}{\sqrt3}

D

2523\frac{25}{2\sqrt3}

Answer

2523\frac{25}{2\sqrt3}

Explanation

Solution

The correct answer is (D) : 2523\frac{25}{2\sqrt3}

Fig.

Altitude of equilateral triangle,
3l2=52\frac{\sqrt3l}{2}=\frac{5}{\sqrt2}
l=523l=\frac{5\sqrt2}{\sqrt3}
Area of triangle
=34l2=34.503=2523=\frac{\sqrt3}{4}l^2=\frac{\sqrt3}{4}.\frac{50}{3}=\frac{25}{2\sqrt3}