A rectangle patio has a length four times its width. It also has a 3-ft wide brick boarder around it. Write a quadratic function to determine the area of the patio and boarder?

Area = 4w² + 30w + 36

Step-by-step explanation:

Let w represent the width of the rectangular patio.

The rectangle patio has a length four times its width. It means that the length of the patio is 4w.

The formula for determining the area of a rectangle is expressed as

Area = length × width

If the boarder is 3 ft, the combined length of the patio and the boarder would be (4w + 3 + 3) = (4w + 6) feet

Also, the combined width of the patio and the boarder would be

(w + 3 + 3) = (w + 6) feet

Therefore, the expression for the area of the patio and boarder is

Area = (4w + 6)(w + 6)

Area = 4w² + 24w + 6w + 36

Area = 4w² + 30w + 36