Answer:
Maximum area enclosed will be 101250 meter².
Step-by-step explanation:
Let the length of the rectangular plot is x meters and the width is y meters.
900 meters is the length of the fence which represents the length of the three sides of the plot.
Therefore,
x + 2y = 900
y = [tex]\frac{1}{2}(900-x)[/tex] meters
Now the area of the rectangular plot will be
A = Length × Width
= (x)(y)
= [tex]\frac{1}{2}x(900-x)[/tex]
= 450x - [tex]\frac{x^{2}}{2}[/tex]
We know for the maximum area we will differentiate the area and equalize it t the zero.
[tex]\frac{dA}{dx}=\frac{d}{dx}(450x-\frac{x^{2}}{2})[/tex]
= 450 - x
For the maximum area, [tex]\frac{dA}{dx}=0[/tex]
Therefore, 450 - x = 0
x = 450
and y = [tex]\frac{1}{2}(900-x)[/tex]
y = [tex]\frac{1}{2}(900-450)[/tex]
y = 450 - 225
= 225 meters
Now the area enclosed A = 450 × 225
A = 101250 meter²
