Question

A rectangle is 4 times as long as it is wide. if the area is 36 square feet, find its perimeter.

Answer 1

30 feet²

Explanation:

Given: Length of rectangle is 4 times as it is wide.

Area of rectangle is 36 feet²

Lets assume the width of rectangle be "w"

∴ Length of the rectangle will be 4w.

Now, using the formula for Area of rectangle to know width and length of rectangle.

Formula; Area of rectangle=
`width* length`

⇒
`36= w* 4w`

⇒
`36= 4w^(2)`

Dividing both side by 4

⇒
`(36)/(4) = w^(2)`

⇒
`9= w^(2)`

Taking square root on both side. remember; √a²=a or -a

⇒
`w=√(9)`

∴
`w=3\ feet\ or -3\ feet, however, \ -3\ is\ ignored\ as\ length\ cannot\ be\ negative`

Next, subtituting the value of width to find legth of rectangle.

Length=
`4w`

∴ Length=
`4* 3= 12\ feet`

Lets find the Perimeter of rectangle now.

Formula; Perimeter=
`2l+2w`, where l = length and w= width

⇒
`Perimeter = 2* 12+2* 3`

⇒
`Perimeter= 24+6`

∴ Perimeter=
`30 feet^(2)`

Hence, perimeter of the rectangle is 30 feet²