SOLUTION: The perimeter of a rectangle is 240 feet. Describe the possible lengths of a side if the area of the rectangle is not to exceed 2700 square feet.

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Question 662391: The perimeter of a rectangle is 240 feet. Describe the possible lengths of a side if the area of the rectangle is not to exceed 2700 square feet.
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

The perimeter P of a rectangle is 240ft.
P=240ft........1
the area of the rectangle A is not to exceed 2700ft%5E2
A%3C=2700ft%5E2......2

240ft=2%28L%2BW%29
240ft%2F2=L%2BW
120ft=L%2BW
L=120ft-W......
A%3C=2700ft%5E2
L%2AW%3C=2700ft%5E2....plug in L and solve for W
%28120ft-W%29%2AW%3C=2700ft%5E2
120Wft-W%5E2%3C=2700ft%5E2
-W%5E2%2B120Wft-2700ft%5E2%3C=0



W=+%28-120ft+%2B-+sqrt%28+14400ft%5E2-10800ft%5E2+%29%29%2F-2+

W=+%28-120ft+%2B-+sqrt%283600ft%5E2%29%29%2F-2+

W=+%28-120ft+%2B-+60ft%29%2F-2+

solutions:

W=+%28-120ft+%2B+60ft%29%2F-2+
W=+%28-60ft%29%2F-2+
highlight%28W=30ft%29+

or
W=+%28-120ft+-+60ft%29%2F-2+
W=+%28-180ft%29%2F-2+
highlight%28W=90ft%29+

now find L
L=120ft-W
L=120ft-30ft
highlight%28L=90ft%29

L=120ft-W
L=120ft-90ft
highlight%28L=30ft%29

so, highlight%28L=90ft%29 and highlight%28W=30ft%29+ or vice versa
since A%3C=2700ft%5E2, any length highlight%28L%3C=90ft%29 will be the
possible length of a side