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

384 feet

Step-by-step 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{ = }(1)/(4)\cdot\text{ L} \\ W\text{ = }(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 + }(L)/(4)) \\ 960\text{ = 2(}(5L)/(4))\text{ = }(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.