The length of a rectangle is 5 inches more than four times its width. If the perimeter of the rectangle is 90 inches, find its length and width.

Answer 1

Let's say W = width and L = length.

A rectangle's perimeter is 2W + 2L, in this case it is equal to 90 inches.

2W + 2L = 90

We are told that L = 4W + 5

Substitute: 2W + 2(4W + 5) = 90

2W + 8W +10 = 90

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10 W +10 = 90

10W = 80

and W = 8 inches

Then 2W + 2*(8) = 90

2W = 74; Therefore W = 37 inches

Check: 2*37 + 2*8 = 90 inches

74 + 16 = 90

90 = 90

Yep.

Bob

Answer 2

Hello Emma. Since we we are told the length is 5 more than 4 times the width, let us call the width variable 'x'. The length would then be 4x + 5.

 

The perimeter, which is 90, is calculated by 2(length + width). Since the length is 4x+5, the width is simply x. Per our problem, 2(x + 5 + 4x) = 90. From here, we add lime terms and solve for x. After doing so, 2(5x + 5) = 90. You can either divide by 2 to both sides or distribute the 2 into 5x+5, it is your preference; it's cleaner if you divide by 2 so, 5x+5=45. Solving for x yields x = 8. Now that we found our width, we now plug 8 back into 4x + 5 to find our length.

  

So width = 8 inches and length = 37 inches