Answer:
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
