The management of a large store has 1,600 feet of fencing to fence in a rectangular storage yard using the building as one side of the yard. If the fencing is used for the remaining three sides, find the area of the largest possible yard.

The largest area of the yard is = 320000 ft²

Step-by-step explanation:

Management has 1600 ft of fencing

They are going to build a rectangular storage (using a building wall as one of the side)

We will find the largest possible yard

Lets call

y the largest side of the rectangle

x the smaller side of the rectangle

Then we have:

Area of rectangle A = x*y

Perimeter of the rectangle (notice one side will be of wall)

P = 1600 ft P = 2x + y y = P - 2x y = 1600-2x

Then

A (x) = x * (1600 - 2x) A (x) = 1600*x - 2x²

So A' (x) = 1600 - 4x A' (x) = 0 1600 - 4x = 0 x = 400 ft

and y = (1600-2*x) ⇒ y = 800 ft

The largest yard is = x * y = 400*800 = 320000 ft²