Math help please

Question

A developer wants to enclose a rectangular grassy lot that borders a city street for parking. If the developer has 252 feet of fencing and does not fence the side along the street, what is the largest area that can be enclosed?

Answer 1

Let x = length of side perpendicular to the road.  Since there are 2 of these, the length of the side parallel to the road is 252-2x (subtract the 2 shorter lengths from the total fence available.

 

Area = length x width

 

A = (252-2x)(x) = 252x-2x²  which is an upside down parabola.  We need to find the vertex to find the maximum area.

 

The x value of a vertex is -b/2a = -225/-2a = 63.

 

The y value (or maximum area) = 252(63) - 2(63)² = 7938 sq ft