Question

The width of a rectangle is 1/4 its length. The perimeter of the rectangle is 960 ft. What is the length, in feet, of the rectangle?

Answer 1

ANSWER

384 feet

EXPLANATION

Let the width of the rectangle be W.

Let the length of the rectangle be L.

We are given that the width is 1/4 of its length. This means that:

$\begin{gathered} W\text{ = }\frac{1}{4}\cdot\text{ L} \\ W\text{ = }\frac{L}{4} \end{gathered}$

The perimeter of a rectangle is given as:

P = 2(L + W)

This means that:

$\begin{gathered} 960\text{ = 2(L + }\frac{L}{4}) \\ 960\text{ = 2(}\frac{5L}{4})\text{ = }\frac{10L}{4} \\ \text{Cross}-\text{ multiply and solve for L:} \\ 4\cdot\text{ 960 = 10 }\cdot\text{ L} \\ \Rightarrow\text{ L =}\frac{4\cdot\text{ 960}}{10} \\ L\text{ = 384 feet} \end{gathered}$

That is the length of the rectangle.