Chapter 6.4, Problem 5P

Solve each word problem

The perimeter of a rectangle is 24 in. and its length is 3 times its width. What are the length and the width of the rectangle?

To determine

To find: The length and width of the rectangle.

Answer to Problem 5P

The length and width of the rectangle are 9 and 3 respectively.

Explanation of Solution

Given:

Perimeter of a rectangle is 24.

The length is 3 times of its width.

Concept used:

The formula to compute the perimeter of a rectangle is:

  $\begin{array}{l}\text{Perimeter = 2}\times \left(l+w\right)\\ \text{Where,}\\ l=\text{ Length}\\ w=\text{Width}\end{array}$

Calculation:

It has been given that length is 3 times of its width. So, the width and length are w and 3w respectively.

The width can be computed as:

  $\begin{array}{c}\text{Perimeter = 2}\times \left(l+w\right)\\ 24=2\times \left(3w+w\right)\\ 24=8w\\ w=3\end{array}$

Now, length can be computed as:

  $\begin{array}{c}L=3w\\ =3\times 3\\ =9\end{array}$

Hence, the required length and width of the rectangle are 9 and 3 respectively.