Consider the triangle with vertices

MATHEMATICS · Single correct · CBSE · Mathematics · Coordinate Geometry · Coordinate Geometry

Problem

Consider the triangle with vertices (2,−1)(2,-1), (a,3)(a,3) and (5,a)(5,a), where a>0a>0. If its area equals 2a2a square units, what is the smaller positive value of aa that satisfies this condition? (a) 77 (b) 3+652\dfrac{3+\sqrt{65}}{2} (c) −3+652\dfrac{-3+\sqrt{65}}{2} (d) 33

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