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
