Question

Mr. Reed is drawing a blueprint of a rectangular patio. The width of the patio is 40 3/4 feet shorter than twice its length. The perimeter of the patio 86 1/2 feet what is the length of the patio?

Answer 1

Length of rectangular patio = 28 feet

Explanation:

Given that:

Length of rectangular patio = x

Width of rectangular patio =
`2x-40(3)/(4)`

Perimeter of rectangular patio =
`86(1)/(2)`

Perimeter of rectangular patio = 2 (length + width )

Putting values in the formula

`86(1)/(2)=2(x+2x-40(3)/(4))\\\\(173)/(2)=2(3x-(163)/(4))\\\\(173)/(2)=2((12x-163)/(4))\\\\(173)/(2)=(12x-163)/(2)\\\\173 = 12x-163\\12x = 173 + 163 \\12x = 336`

Dividing both sides by 12

`(12x)/(12)=(336)/(12)\\x=28`

Hence,

Length of rectangular patio = 28 feet