Question

A rectangle is 5 times as long as it is wide. The perimeter is 24 feet. Find the dimensions.The length isfeet where the width isfeet.

Answer 1

The length is 10 feet where the width is 2 feet.

Step-by-step explanation:

Let l represent the length of the rectangle

Let w represent the width of the rectangle

From the question, we have;

`\begin{gathered} l=5w \\ Perimeter(P)=24\text{ feet} \end{gathered}`

Recall that the formula for the perimeter(P) of a rectangle is given as;

`P=2(l+w)`

Let's now substitute P with 24 and l with 5w in the above equation and solve for w as seen below;

`\begin{gathered} 24=2(5w+w) \\ 24=2(6w) \\ 24=12w \\ (24)/(12)=(12w)/(12) \\ 2=w \\ \therefore w=2\text{ feet} \end{gathered}`

So the width of the rectangle is 2 feet

The length of the rectangle can be determined as seen below;

`\begin{gathered} l=5w \\ l=5*2 \\ l=10\text{ feet} \end{gathered}`

So the length of the rectangle is 10 feet