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 the rectangular portion of a football field enclosed by a running track, we will follow these steps:

### Step 1: Understand the Problem
We have a running track with a total perimeter of 440 ft, enclosing a rectangular field with semicircles at each end. We need to find the dimensions of the rectangle that maximize its area.

### Step 2: Set Up the Variables
Let:
- \( x \) = length of the rectangular portion
...