please help med im lost

Question

Solve this application problem using a system of equations: The perimeter of a rectangular building is 234 feet. The width is 27 feet shorter than the length. What are the dimensions?

Answer 1

Answer 2

Formula for a perimeter is

2L + 2W = P

The second equation you have is W = L - 27

You can substitute L - 27 for W in the first equation.

P = 234 = 2L + 2(L - 27)

Distribute

234 = 2L + 2L - 54

Combine like terms

234 = 4L - 54

Add 54 to both sides

234 + 54 = 4L - 54 + 54

288 = 4L

Divide both sides by 4

288/4 = 4L/4

72 = L

So the length is 72 feet.

The width is 27 feet shorter than the length.

W = L - 27 = 72 - 27 = 45

You can double check your work by plugging L and W into 2L + 2W to verify you get 234

2(72) + 2(45) = 144 + 90 = 234