An elementary school is creating a rectangular garden on the side of the school building. The school has raised money to purchase 1000 feet of fence. In order to maximize the area they are using the building for one side and therefore need to use the fencing for the other three sides of the garden. Find the dimensions the school should use to maximize the area of the garden.

Step-by-step explanation:

Given

--- perimeter

Required

The dimensions that maximize the area

Let

Such that:

---- Because one side is from the school building

This gives:

Make L the subject

The area is then calculated as:

Substitute:

Open bracket, then set A to 0

Rewrite as:

Assume the form of the above equation is:

The value of W that maximizes it is:

Where

So:

Recall that:

So, the dimensions that maximize the area is:

3/4 ÷ 3/4

step-by-step explanation:

basically divide any proper fraction with itself to fit the criteria.

so if we are using 3/4, then:

3/4 ÷ 3/4 = 1

so 1 is the quotient.

and the numerators for both these fractions is 3.   and if we divide the numerators:

3 ÷ 3 = 1

we see that quotient is equal to our original quotient as well.

you would need to know all the numbers that are on there

step-by-step explanation: