SOLUTION: One-fifth the perimeter of a building is 50 feet. The length of the building is 30 feet longer than the width. What is the area of the building?

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Question 759023: One-fifth the perimeter of a building is 50 feet. The length of the building is 30 feet longer than the width. What is the area of the building?
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

One-fifth the perimeter of a building is 50ft.
P=2%28L%2BW%29....eq.1......the perimeter of a building
One-fifth of the perimeter is P%2F5=50ft; so, the perimeter of a building is P=50ft%2A5 => P=250ft
then
250ft=2%28L%2BW%29
250ft%2F2=%28L%2BW%29
125ft=%28L%2BW%29...solve for L
L=125ft-W......eq. 1a
if the length of the building L is 30ft longer than the width W, than
L=W%2B30ft.......plug in eq.1a
W%2B30ft=125ft-W......eq. 1a....solve for W
W%2BW=125ft-30ft
2W=95ft
W=95ft%2F2
highlight%28W=47.5ft%29
now find L
L=47.5ft%2B30ft
highlight%28L=77.5ft%29
the area of the building is A=L%2AW
A=77.5ft%2A47.5ft
highlight%28A=3681.25ft%5E2%29