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GATE 2014 EC (EC4) – Question 39

Engineering Mathematics · Calculus · 2 marks · Multiple choice

For a right triangle, the sum of the hypotenuse and one side is fixed. What angle between that side and the hypotenuse maximizes area?

  1. 12°
  2. 36°
  3. 60°
  4. 45°

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Show answer and explanation

Correct answer: (C) 60°

Explanation

Let hypotenuse c, specified side a, and a+c=S. The other side is√(c²−a²)=√[S(2c−S)]. The squared area is proportional to(S−c)²(2c−S). Differentiating yields the interior maximum c=2S/3and a=S/3. Thus cosθ=a/c=1/2and **θ=60°,C**.