Question

The owner of a motel has 5000 m of fencing and wants to enclose a rectangular plot of land that borders a straight highway. if she does not fence the side along the highway, what is the largest area that can be enclosed?

Answer 1

The perimeter in this case is:
y + 2x = 5000
The area is:
A = x * y
We rewrite the area:
A = x * (5000-2x)
A = 5000x-2x ^ 2
We derive:
A '= 5000-4x
We equal zero and clear x:
0 = 5000-4x
4x = 5000
x = 5000/4
x = 1250
We look for the other dimension:
y = 5000-2x
y = 5000-2 (1250)
y = 5000-2500
y = 2500
Then, the area will be:
A = (2500) * (1250)
A = 3125000 m ^ 2
Answer:
The largest area that can be enclosed is:
A = 3125000 m ^ 2