# The perimeter of a rectangle is 24 inches, how do you find the dimensions if its length is 3 times greater than its width?

Aug 4, 2015

Length: 9 inches
Width: 3 inches

#### Explanation:

You use the information given to you to write a system of two equations.

The perimeter of a rectangle is equal to the sum of its length and its width, multiplied by $2$

$\textcolor{b l u e}{P = 2 \cdot \left(L + w\right)}$

In your case, you know that

$2 \left(L + w\right) = 24$

This will be your first equation.

Now focus on the fact that its length is 3 times greater than its width. This can be written like this

$L = 3 \cdot w$

$\left\{\begin{matrix}2 \left(L + w\right) = 24 \\ L = 3 w\end{matrix}\right.$

To solve for the length and width of the rectangle, use the expression you have for $L$ in the first equation to get $w$

$2 \cdot \left(3 w + w\right) = 24$

$2 \cdot 4 w = 24 \implies w = \frac{24}{8} = \textcolor{g r e e n}{3}$

This means that $L$ is equal to

$L = 3 \cdot 3 = \textcolor{g r e e n}{9}$