Adeveloper 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?

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 :)

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