Question

Wayne is hanging a string of lights 63 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 7 feet longer than twice its width. Find the length and width of the patio.

Answer 1

We will determine the length and width of the patio as follows:

*First: We write the equations that we can derivate from the text, those are:

`63=w+l`

&

`l=2x+7`

&

`w=x`

*Second: We will replace this last two equations in the first one and solve for x:

`63=2(x)+(2x+7)\Rightarrow63=4x+7`
`\Rightarrow56=4x\Rightarrow14=x`

So, we have that the width of the patio is 14 feet long.

*Third: We determine the length:

`l=2(14)+7\Rightarrow l=35`

So, we have that the lenght of the patio is of 35 feet long.