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 = \(\frac{1}{2}(900-x)\) meters
Now the area of the rectangular plot will be
A = Length × Width
= (x)(y)
= \(\frac{1}{2}x(900-x)\)
= 450x - \(\frac{x^{2}}{2}\)
We know for the maximum area we will differentiate the area and equalize it t the zero.
\(\frac{dA}{dx}=\frac{d}{dx}(450x-\frac{x^{2}}{2})\)
= 450 - x
For the maximum area, \(\frac{dA}{dx}=0\)
Therefore, 450 - x = 0
x = 450
and y = \(\frac{1}{2}(900-x)\)
y = \(\frac{1}{2}(900-450)\)
y = 450 - 225
= 225 meters
Now the area enclosed A = 450 × 225
A = 101250 meter²
