Final answer:
The width of the patio is approximately 5.7 feet and the length is approximately 16.4 feet.
Step-by-step explanation:
To find the dimensions of Wayne's patio, we can set up a system of equations based on the given information. Let's denote the width of the patio as 'w'. Given that the length of the patio (the side along the house) is five feet longer than twice its width, we can express this as: length = 2w + 5.
We also know that the string of lights around the patio is 45 feet long, so the perimeter of the patio is 45 feet. The perimeter of a rectangle is given by the formula P = 2(length + width). Setting up the equation and substituting the expression for the length, we have: 45 = 2(2w + 5 + w). Solving this equation will give us the value of 'w', which represents the width of the patio. Once we have the value of 'w', we can substitute it into the expression for the length to find the actual dimensions of the patio.
Let's solve the equation: 45 = 2(3w + 5). Distributing the 2, we get: 45 = 6w + 10. Subtracting 10 from both sides of the equation, we have: 35 = 6w. Dividing both sides by 6, we get: w = 5.7.
Therefore, the width of the patio is approximately 5.7 feet. To find the length, we substitute this value of 'w' into the expression for the length: length = 2(5.7) + 5 = 11.4 + 5 = 16.4.
Therefore, the length of the patio is approximately 16.4 feet. The dimensions of the patio are approximately 16.4 feet by 5.7 feet.