Question

farmer ed has 900 meters of fencing and wants to enclose a rectangular plot that borders on the river. if farmer ed does not fence the side along the river . find the length and the width of the plot that will maximize the area. what is the largest area that can be enclosed.

Answer 1

the largest area can be enclosed by 300 meters per side along the fence 
hoped this helped

Answer 2

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