A running track of 440 ft is to be laid out enclosing a football field, the shape of which is a rectangle with a semi-circle at each end. If the area of the rectangular portion is to be maximum, then find the length of its sides.

Explanation

To solve the problem of maximizing the area of a rectangular football field enclosed by a running track, we will follow these steps:

### Step 1: Define the Variables
Let:
- \( x \) = length of the rectangular portion
- \( r \) = radius of the semicircles at each end

### Step 2: Set Up the Perimeter Equation
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