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

Length: 9 inches
Width: 3 inches

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

##{( 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)##

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