Question

In the following exercises, translate to a system of equations and solve.

Wayne is hanging a string of lights 45 feet long around the three sides of his rectangular 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.

Short answer

The measure of length and width of the patio are 25, 10 feet respectively.

Step-by-step solution

Step 1. Given Information

The given data is that Wayne is hanging a string of lights 45 feet long around the three sides of his rectangular 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.

Step 2. Calculation

Let x be the length and y be the width.

The length of his patio, is five feet longer than twice its width that is $x=2y+5--\left(1\right)$

The string of lights 45 feet long around the three sides of his rectangular patio, which is adjacent to his house that is $x+2y=45--\left(2\right)$

Solve the equations by substituting equation (1) in equation (2) to find the value of y.

$$\begin{gathered} 2y+5+2y=45 \\ 4y=40 \\ y=10 \end{gathered}$$

Substitute the value of y in equation (1) to obtain the value of x.

$$\begin{gathered} x=2\left(10\right)+5 \\ x=20+5 \\ x=25 \end{gathered}$$