You just discovered that you have 100 feet of fencing and you have decided to make a rectangular garden. What is the largest area you can enclose using the materials you have? You must set up an equation and solve.

The area is:

A = x * y

The perimeter is:

P = 2x + 2y = 100

We clear y:

2y = 100-2x

y = 50-x

We write the area in terms of x:

A (x) = x * (50-x)

Rewriting:

A (x) = 50x-x ^ 2

Deriving:

A ' (x) = 50-2x

We equal zero and clear x:

50-2x = 0

x = 50/2

x = 25

Then, the other dimension is given by:

y = 50-x

y = 50-25

y = 25

Therefore, the largest area is:

A = (25) * (25)

A = 625 feet ^ 2

Answer:

the largest area you can enclose using the materials you have is:

A = 625 feet ^ 2