Question

The length of a rectangle is 12 ft longer than twice the width. If the perimeter is 96 ft, find the length and width of the rectangle

Answer 1

Let the length of the rectangle = L

Width of the rectangle = w

The length of a rectangle is 12 ft longer than twice the width.

So,

`l=12+2w`

The perimeter of the rectangle is given by the formula:

`P=2(l+w)`

Given perimeter = 96 ft

Substitute with the perimeter and the equation of the length into the equation of the perimeter

So,

`2(12+2w+w)=96`

Solve the equation to find w:

`\begin{gathered} 12+3w=(96)/(2) \\ 3w+12=48 \\ 3w=48-12 \\ 3w=36 \\ w=(36)/(3)=12 \end{gathered}`

So, the length of the rectangle =

`l=12+2w=12+24=36`

So, the answer will be:

Length = 36 ft

Width = 12 ft