The length of a rectangular patio is 7 feet more than its width, w. The area of a patio, A (w), can be represented by function

The function that represents the area of the the patio is A (w) = w² + 7w.

Step-by-step explanation:

The area of a rectangle is given by the following formula:

area = width*length

In this case the length is 7 feet more than the width, using "l" for length and "w" for width we have:

l = w + 7

Using this on the formula we have:

A (w) = area = w * (w+7) = w² + 7w

The function that represents the area of the the patio is A (w) = w² + 7w.