Question

The length of a rectangle is one unit shorter than one-sixth of the width, x.

Which expression represents the perimeter of the rectangle?

Answer 1

`P=2l+2w`

`P=2((x)/(6)-1)+2(x)`

`P=(2x)/(6)-2+2x`

`P=(x)/(3)-2+2x`

`P=2(1)/(3)x-2`

Answer 2

Perimeter =
`(7)/(3)x-2`

Explanation:

The length of a rectangle is one unit shorter than one-sixth of the width, x

LEts x be the width of the rectangle

Length is 1 unit shorter than 1/6 of width

`Length = (1)/(6) x-1`

Perimeter of the rectangle = 2(length ) + 2(width)

Replace length and width

Perimeter =
`2((1)/(6) x-1)+2x`

Simplify it

Perimeter =
`(1)/(3) x-2+2x`

`(1)/(3) x+2x=(1)/(3)x+(6)/(3) x=(7)/(3)x`

Perimeter =
`(7)/(3)x-2`