Q26 of 39 Page 1

If the sum of lengths of the hypotenuse and a side of a right-angled triangle is given, show that the area of the triangle is maximum, when the angle between them is

Let ABC be the right triangle with hypotenuse AC = y, base BC = x and x + y = k; a constant


θ, be the angle between AC and BC.


Area of the triangle;



Now, for maxima or minima, ,


Therefore, differentiating both sides, we get,




Differentiating again, we get,






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