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
\(\frac{25}{4\sqrt3}\)
\(\frac{25\sqrt3}{2}\)
\(\frac{25}{\sqrt3}\)
\(\frac{25}{2\sqrt3}\)
The Correct Option is D
Solution and Explanation
The correct answer is (D) : \(\frac{25}{2\sqrt3}\)
Altitude of equilateral triangle,
\(\frac{\sqrt3l}{2}=\frac{5}{\sqrt2}\)
\(l=\frac{5\sqrt2}{\sqrt3}\)
Area of triangle
\(=\frac{\sqrt3}{4}l^2=\frac{\sqrt3}{4}.\frac{50}{3}=\frac{25}{2\sqrt3}\)
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