A rectangular 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 1500 m of wire at your disposal, what is the largest area you can enclose, and what are its dimensions

Step-by-step explanation:

Let x be the length and y be the width of the rectangular plot.

The plot is bounded on one side by a river and on the other three sides by a single-strand electric fence. It means,

x+2y = 1500

x = 1500 - 2y ....(1)

We know that the area of a rectangular plot is given by :

A = xy ....(2)

Put the value of x from equation (1) in (2)

.....(3)

For largest area, differentiate above area equation wrt y.

Put the value of y in equation (1).

x = 1500-2(375)

= 750 m

Put the value of y in equation (3).

Hence, the largest area is 281250 m² and its dimensions are 750 m and 375 m.