Prove that the area of right-angled triangle of given hypotenuse is maximum when the triangle is isosceles.

Explanation

To prove that the area of a right-angled triangle with a given hypotenuse is maximum when the triangle is isosceles, we can follow these steps:

### Step 1: Define the Triangle
Let the hypotenuse of the right triangle be \( A \). Denote one of the legs as \( x \) and the other leg as \( y \). According to the Pythagorean theorem, we have:
\[ x^2 + y^2 = A^2 \]

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