Problema Solution
A developer wants to enclose a rectangular grassy lot that borders a city street for parking. If the developer has 320 feet of fencing and does not fence the side along the street, what is the largest area that can be enclosed?
Answer provided by our tutors
Assuming that the developer fences three sides of a rectangle, we can define dimensions x and y such that:
2x + y = 320
y = 320 - 2x
A = xy the area of the rectangle
A = x(320 - 2x)
A = -2x^2 - 320x
We need to find the maximum of the parabolic function A = -2x^2 - 320x
A max= c - b^2/(4a), a = -2, b = -320, c = 0
A max = - (-320)^2/(4*(-2))
A max = 12,800 ft^2
The largest area that can be enclosed is 12,800 ft^2.