SOLUTION: A stage has an area of 840 square feet. Its perimeter is 122 feet. What are the dimensions of the stage?

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Question 957710: A stage has an area of 840 square feet. Its perimeter is 122 feet. What are the dimensions of the stage?

Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
A=area=840ft^2; P=perimeter=122ft; L=length; W=width
P=2(L+W)
122ft=2(L+W) Divide each side by 2.
61ft=L+W Subtract W from each side
61ft-W=L
A=L%2AW Substitute for L
840ft%5E2=%2861ft-W%29%28W%29
840ft%5E2=-W%5E2%2B61W Subtract 840ft^2 from each side.
0=-W%5E2%2B61W-840ft%5E2 Multiply by (-1)
0=W%5E2-61W%2B840ft%5E2
0=%28W-21%29%28W-40%29
W-21=0 or W-40=0
W=21ft or W=40ft ANSWER 1: The width is 21 feet.
L=61ft-W=61ft-21ft=40ft ANSWER 2: The length is 40 feet.
CHECK:
A=L*W
840ft^2=(40ft)(21ft)
840ft^2=840ft^2