Question

A developer wants to enclose a rectangular grassy lot that borders a city street for parking. if the developer has 256 feet of fencing and does not fence the side along the​ street, what is the largest area that can be​ enclosed?

Answer 1

Let the lenght perpendicular to street = x

Means lenght two sides will be x and x

Another side of retangle will be = 256 - 2x

Area of rectangle will be= A = x * (256-2x) = 256 x - 2 x^2

For maximum area, dA/dx = 0

d/dx (256 x - 2 x^2) = 0

256 - 4 x = 0

4 x = 256

x = 64 feet

Means one side is 64 feet

Another side will be = 256 - 2 * 64 = 128

Now we have two sides of rectangle 64 and 128

Area = 128 * 64 = 8192 square feet : Answer

Hope it will help :)