Question

Wayne is hanging a string of lights 78 feet long around the three sides of his piano, which is adjacent to his house. The length of his patio, the side along the house, is 6 feet longer than twice it’s width. Fine the length and width of the patio.

Answer 1

The width is 18 feet and the length is 42 feet

Explanation:

Let x feet be the width of the patio. The length of the patio is 6 feet longer than twice it’s width, then the length of the patio is 2x+6 feet.

Wayne is hanging a string of lights 78 feet long around the three sides of his patio, which is adjacent to his house. The side with length 2x+6 feet is adjacent to the house, so Wayne is hanging a string along three sides with lengths x ft, x ft and 2x+6 ft.

Hence,

`x+x+2x+6=78\\ \\4x=78-6\\ \\4x=72\\ \\x=18\ ft`

The width
`= 18` ft

The length
`=2\cdot 18+6=36+6=42` ft