Hello, anitha!

The hypotenuse of a right-angled triange has the length of 10cm.

Find an expression for the area of the triangle in terms of

For what value of is the area a maximum and what is this maximum area?

A right triangle can be inscribed in a semicircle. Code:

* * * C
* *
* * :**
* * h: **
* θ : *
A * - - - - - - - + - * B
10

The base of the triangle is 10.

Hence, the area is: .

Therefore: .

The area is a maximum when is a maximum.

. . This occurs when (radius) . . .

Therefore, the maximum area is: .