Question

A security fence encloses a rectangular area on one side of a park in a city. three sides of fencing are? used, since the fourth side of the area is formed by a building. the enclosed area measures 392392 square feet. exactly 5656 feet of fencing is used to fence in three sides of this rectangle. what are the possible dimensions that could have been used to construct this? area?

Answer 1

Let x = length of the park
Let y = width of the park

Because the area is 392392 ft², therefore
xy = 392392          (1)
Because three sides of fencing measure 5656 ft, therefore
2x + y = 5656        (2)
That is
y = 5656 - 2x          (3)
Substitute (3) into (1).
x(5656 - 2x) = 392392
5656x - 2x² = 392392
2x² -5656x + 392392 = 0
x² - 2828x + 196196 = 0

Solve with the quadratic formula.
x = (1/2)*[2828 +/- √(2828² - 4*196196)]
   = 2756.83 or 71.17

Answer:
The possible dimensions are 2756.8 ft and 71.2 ft (nearest tenth)