A rectangular field, bounded on one side by a building, is to be fenced in on the other three sides. if 3000 feet of fence is to be used, find the dimensions

The question is missing the detail, it is to find the dimensions of the largest field that can be fenced in.

The formula for area is : A = xy

The perimeter of the fencing is equal to the sum of two widths and the length: 2x + y = 3000

Now, solve the second equation: y = 3000 - 2x

When you plug this expression to the formula for the area, we will get:

A = x (3000-2x) = 3000x - 2x^2

Next take the derivative and equal it to 0: dA/dx = 3000 - 4x = 0

Now solve for x, it will give us 750.

Find the second derivative.

d^2 A / dx^2 = - 4

since we have a negative result, x = 75 - is a maximum. Then plug this in to x:

3000 - 2 (750) = 1500. The largest field will measure 750 ft by 1500 ft.