Problema Solution
A security fence encloses a rectangular area on one side of a park. Three sides of fencing are used, since the fourth side of the area is formed by a building. The enclosed area measures 648 square feet. Exactly 72 feet of fencing is used to fence in the three sides of the rectangle. What are the possible dimensions that could have been used to construct this area?
Shorter dimension of the fenced area is ___ft.
Longer dimension of the fenced are is ____ft.
Answer provided by our tutors
Let 'x' and 'y' represent the dimensions of the rectangular area, x>=0, y>=0.
The fencing is 72 ft long:
2x + y = 72 (we assume the building is on the fourth side with length y)
y = 72 - 2x
The area is 648 ft^2:
x*y = 648
Plug y = 72 - 2x into x*y = 648:
x*(72 - 2x) = 648
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click here to see the equation solved for x
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x = 18 ft
y = 72 - 2*18
y = 36 ft
Shorter dimension of the fenced area is 18 ft.
Longer dimension of the fenced are is 36 ft.