NDA 2021 Mathematics question

A 24 cm long wire is bent to form a triangle with one of the angles as 60°. What is the altitude of the triangle having the greatest possible area?

Answer: (A)

Solution

Let the sides containing the 60° angle be and , and the third side . Area , so we must maximise . Let ; then and by the cosine rule . So ,

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Question ID VK-033574