A figure consists of a semi-circle with a rectangle on its diameter. Given the perimeter of the figure, find its dimensions in order that the area may be maximum.

Explanation

To solve the problem of maximizing the area of a figure consisting of a semicircle with a rectangle on its diameter, given a fixed perimeter, we will follow these steps:

### Step 1: Define the Variables
Let:
- \( R \) = radius of the semicircle
- \( x \) = breadth of the rectangle
- The length of the rectangle will be \( 2R \) (since it spans the diameter of the semicircle).

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