Prove that the area of a right angled triangle of given hypotenuse is maximum when the

triangle is isosceles

Let h be the hypotenuse of the right-angles triangle, and let x be it altitude.


Base of the triangle 

Let A be the area of the triangle. Then,

For maximum or minimum, we have


Thus, A is maximum when 

Hence, A maximum when the triangle is isosceles.

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