A company will enclose a rectangular area of 12,800 square feet in the rear of its plant.One side will be bounded by the building and the other three sides by fencing.Suppose that 400 feet of fencing will be used and that the side of the building has a length of 100 ft.What will be the dimension (in feet)of the side of the rectangle that is opposite the building?
A) 20
B) 40
C) 60
D) 80
E) 90

Question

Quizplus · Accepted Answer

The total perimeter of the rectangle is the sum of the three sides of fencing plus the side of the building that is already there. Since one side is the building, and it's 100 feet, and we have 400 feet of fencing for the other three sides, the total perimeter is 400 + 100 = 500 feet. If we let x be the length of the two sides that are fenced (not the side opposite the building), then the equation for the perimeter is 2x + 100 + side opposite the building = 500. The side opposite the building is also 100 feet because it's parallel to the side of the building, making the equation 2x + 200 = 500. Solving for x gives x = (500 - 200) / 2 = 150 / 2 = 75 feet for each of the two sides. However, the question asks for the dimension of the side opposite the building, which is 100 feet, matching option D.

A Company Will Enclose a Rectangular Area of 12,800 Square