Question

The width of a rectangle is
`(3)/(4)` its length. The perimeter of the rectangle is 420 ft. What is the length, in feet, of the rectangle?

Answer 1

The width of a rectangle is 3/4 its length.

`w=(3)/(4)l`

The perimeter of the rectangle is 420 ft.

Recall that the perimeter of a rectangle is given by

`P=2(w+l)`

Let us substitute the value of the given perimeter and the width

`\begin{gathered} P=2(w+l) \\ 420=2((3)/(4)l+l) \end{gathered}`

Now simplify and solve for length

`\begin{gathered} 420=2((3)/(4)l+l) \\ 420=(3)/(2)l+2l \\ 420=3.5l \\ l=(420)/(3.5) \\ l=120\: ft \end{gathered}`

Therefore, the length of the rectangle is 120 feet.