The perimeter of a rectangular window is 28 ft. The width is 6 ft more than the length. What are the dimensions of the window?

Question

The perimeter of a rectangular window is 28 ft. The width is 6 ft more than the length. What are the dimensions of the window?

Answer 1

Let L = the length of the window and W = its width.  We have two unknowns (L and W), so we need two equations to solve for them.

 

Equation 1: The perimeter of a rectangular window is 28 ft:  28 = 2L + 2W

Equation 2: The width is 6 ft more than the length:  W = L + 6

 

Let's use equation 2 to substitute L+6 for W in equation 1:

 

28 = 2L + 2W            [Equation 1]

28 = 2L + 2(L+6)       [Substituted L+6 in place of W]

28 = 2L + 2L + 12

16 = 4L

4 = L

 

W = L+6

W = 4 + 6

W = 10

 

Check:

28 = 2L + 2W

28 = 2(4) + 2(10)

28 = 28                  CHECK!

Answer 2

Hello, thank you for taking the time to post your question!

The key on this type of question is to set up equations to relate the variables to one another based on the information given. For this one that means

2L + 2W = 28        since the perimeter is 28

W = L + 6              since the width is 6 more than the length

I would take the second equation and substitute it into the first equation in order to solve for the value of L. when I do that I get L = 4, meaning that W = 4 + 6 = 10

So the dimensions of the window are the length is 4 ft and the width is 10 ft.

I hope that helps get you moving in the right direction! Feel free to reach out if you have any additional questions beyond that :)