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?

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