Wayne is hanging a string of lights 59 feet long around the three sides of his patio, which is adjacent to his house. The length of his patio, the side along the house, is 3 feet longer than twice its width. Find the length and width of the patio.

The width is 18 feet and the length is 42 feet

Step-by-step explanation:

Let x feet be the width of the patio. The length of the patio is 6 feet longer than twice it’s width, then the length of the patio is 2x+6 feet.

Wayne is hanging a string of lights 78 feet long around the three sides of his patio, which is adjacent to his house. The side with length 2x+6 feet is adjacent to the house, so Wayne is hanging a string along three sides with lengths x ft, x ft and 2x+6 ft.

x+x+2x+6=78

4x=78-6

4x=72

divide both sides by 4

x=18 ft

The width  18 ft

2*18+6=36+6=42 ft

The length  42 ft