If the sum of lengths of hypotenuse and a side of a right angled triangle is given, show that area of triangle is maximum, when the angle between them is `pi/3dot`

Explanation

To solve the problem, we need to show that the area of a right-angled triangle is maximized when the angle between the hypotenuse and one of the sides is \(\frac{\pi}{3}\) radians (or 60 degrees).

### Step-by-step Solution:

1. **Draw the Right-Angled Triangle**:
- Let triangle ABC be a right-angled triangle with the right angle at B. Let AB = x (one side), BC = y (the hypotenuse), and AC be the other side.

2. **Set Up the Equation for the Sum**:
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