Mathematics: Arectangular plot of farmland will be bounded on one side by a river and on the other three sides by a single-strand electric fence. with 2100 m of wire at your disposal, what is the largest area you can enclose, and what are its dimensions?

On the y-axis, between Quadrant 1 and 2.Step-by-step explanation:...

Arectangular plot of farmland will be bounded on one

tonya3498

12.01.2022

525 x 1,050

A = 551,250 m²

Step-by-step explanation:

Let 'L' be the length parallel to the river and 'S' be the length of each of the other two sides.

The length of the three sides is given by:

$2S+L=2,100\\ L=2100-2S$

The area of the rectangular plot is given by:

$A=S*L\\A=S(2100-2S)\\A=2100 S -2S^2$

The value of 'S' for which the area's derivate is zero, yields the maximum total area:

$\frac{dA(S)}{dS}=\frac{d(2100 S -2S^2)}{dS}\\0= 2100 - 4S\\S=525$

Solving for 'L':

$L=2100-(2*525)\\L=1,050$

The largest area enclosed is given by dimension of 525 m x 1,050 and is:

$A = 525*1,025\\A=551,250\ m^2$

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