Wayne is hanging a string of lights 45 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 five feet longer than twice its width. Find the length and width of the patio.

The length and width of the patio are 18¹/₃ feet and 6²/₃ feet respectively.

Step-by-step explanation:

Let L and W be the length and width of the patio respectively. Since the patio is a rectangle, its perimeter, P = 2(L + W). This perimeter equals the length of string of lights which is 45 ft.

Now, the length of his patio, the side along the house, is five feet longer than twice its width implies that L = 2W + 5.

Substituting L into P, we have

P = 2(L + W)

= 2(2W + 5 + W)

= 2(3W + 5)

= 6W + 5

Since P = 45 feet,

6W + 5 = 45

6W = 45 - 5

6W = 40

W = 40/6

W = 20/3 feet

W = 6²/₃ feet

Since L = 2W + 5, substituting W = 20/3 into L, we have

L = 2W + 5

= 2(20/3) + 5

= 40/3 + 5

taking the L.C.M, we have

= (40 + 15)/3

= 55/3 feet

= 18¹/₃ feet

So, the length and width of the patio are 18¹/₃ feet and 6²/₃ feet respectively.

i hope this is what you were looking for.

see attached graph