Q 108 - Intermediate Algebra

Question

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.

Step-by-Step Solution

Answer

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

Step 1 Given information is,

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.

Step 2 To find:

The length and the width of the patio.

Step 3 let us consider,

$l$ represents the length of the patio

$w$ represents the width of the patio.

It is given that,

Wayne is hanging a string of lights 45 feet long around the three sides of his patio, which is adjacent to his house.

The above lines gives an equation,

$l+2w=45$.

Also it is given that, The length of his patio, the side along the house, is five feet longer than twice its width.

So,$l=5+2w$.

Step 4 From the step 3 ,

The obtained linear equations are,

$$\begin{gathered} l+2w=45 \\ l=5+2w \end{gathered}$$

Now substitute $l=5+2w$ in the equation $l+2w=45$.

$$\begin{gathered} 5+2w+2w=45 \\ 5+4w=45 \\ 4w=45-5 \\ 4w=40 \\ w=\frac{40}{4} \\ w=10 \end{gathered}$$

Step 5 Find the value of l .

Substitute the value of $w$ in the equation $l=5+2w$.

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