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

1 Answer
Aug 4, 2015

Answer:

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#

#color(blue)(P = 2 * (L + w))#

In your case, you know that

#2(L+w) = 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 * w#

Your system will be

#{( 2(L+w) = 24), (L = 3w) :}#

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 * ( 3w + w) = 24#

#2 * 4w = 24 => w = 24/8 = color(green)(3)#

This means that #L# is equal to

#L = 3 * 3 = color(green)(9)#