# What is the largest rectangular area that can be enclosed with 200 m of fence?

1
by cupiecupie
You lack details i think.
oh sorry I'd just found the right solution for this.

2014-11-17T11:36:47+08:00
Let me try this.

The formula for Perimeter will be

Perimeter: 2w + 2l = 200m

For Area

Area: A = l * w

We must find the value for either length or width.

2w + 2l = 200

Transpose 2l

2w = 200 - 2l

Divide by 2 both to eliminate 2 in 2w

2w/2 = (200 - 2l)/2

Therefore

Width = 100 - l

Substitute the value to the Area formula

A = l(100 - l)

Therefore

Area = 100l - l²

Since Area represents a quadratic equation () in terms of l, we will re-write A in function form with the exponents in descending order:

A(l) = -l² + 100l (new formula of Area)

Formula will be like this

Length(l) = -b/2a

where a = -1 and b = 100

Let's now substitute the values

l = -(100)/[2(-1)]

Multiply 2 to -1

l = -100/-2

Divide

Therefore

Length = 50 meters(It will be positive since dividing like terms will be positive)

Now let's substitue the value of Length to the new formula of Area

A(l) = -l² + 100l

A = -(50)² + 100(50)

Multiply 100 and 50; Get the square of 50

A = -(2500) + 5000

Make 2500 negative

A = -2500 + 5000

Solve

Therefore

Area = 2, 500 square meters

Now let's get the real value of width

Width = 100 - l

w = 100 - 50

Therefore

Width = 50 meters

There you have it:

Length and width of the rectangular area would be 50 meters each.

While the total Area that can be enclosed would be 2, 500 meters.

Let's check if Area is really 2, 500 meters

Area = Length * Width

A = 50 * 50

Therefore

Area = 2, 500 meters ◘ Correct

I hope it helps