The length of a rectangle is five times its width. If the perimeter of the rectangle is 72 in , find its area.

Question

The length of a rectangle is five times its width.
If the perimeter of the rectangle is
72in, find its area.

Answer 1

Here's what we know:

P_r = 2L + 2w (perimeter of a rectangle is the two lengths plus two widths)

A_r = Lw (area of a rectangle is length times width)

L = 5w (length is 5 times the width)

P = 72

 

Since we have values for some of our variables, let's plug them in:

72 = 2(5w) + 2w

distribute:

72 = 10w + 2w

combine like terms

72 = 12w

divide by 12:

6 in = w

 

L = 5 * 6

L = 30 in

 

check:

2 * 30 + 2 * 6 = 72

60 + 12 = 72

72 = 72

 

Now that we know w and L, we can find the area:

6 in * 30 in = 180 in²