the width of a rectangle is 6 inches shorter than the length. The perimeter is 48 inches. find the length and width

Question

I've gone over this question multiple times but i still fail to answer the problem. Need help!

Answer 1

Perimeter equals Length plus Width plus Length plus Width, or P = L + W + L + W. Combine like terms and you get:

P = 2L + 2W. We are told that the Width is 6 inches shorter than the Length, so: W = L - 6. Rewrite the equation like this: P = 2L + 2(L - 6)

Plug in perimeter and distribute the 2: 48 = 2L + 2L - 12

Combine like terms: 48 = 4L - 12

Add 12 to both sides and you get: 60 = 4L

Divide both side by 4: 15 = L

Length = 15 inches

Width = L - 6 or 15 - 6 or 9 inches

Check your work by plugging your answers into the equation:

P = 2L + 2W

48 = 2(15) + 2(9) = 30 + 18 = 48

 

Answer 2

length of the rectangle = x

width of the rectangle = (x - 6)

 

P = 2L + 2W for a rectangle, where L = length and W = width

 

P = 48 according to the problem

 

48 = 2x + 2(x - 6)

 

48 = 2x + 2x - 12

 

48 = 4x - 12

 

4x = 60

 

x = 15

 

The length is 15 in. and the width is 15 - 6 = 9 in.