Farmer Ed has7500 meters of fencing, and wants to enclose a rectangular plot that borders on a river. If Farmer Ed does not fence the side along the river, what is the largest area that can be enclosEd?

7,031,250 m^2

Step-by-step explanation:

We know that:

Area of a rectangle = length x width

Also, since the rectangular plot shares a border with a river so Farmer Ed only needs to fence rest of the three sides therefore, we can write it as:

F = x + 2y

7500 = x + 2y

Solving this equation for x, we get:

x = 7500 - 2y - - - (i)

Now substitute this value of x in the Area of rectangle:

Area = (7500 - 2y) * y

Area = - 2y^2 + 7500y - - - (ii)

The coefficient of - 2 means that the largest area will be at:

-7500 / [2 (-2) ] = 1875 so y = 1875

So substituting this value of y in the equation (i) we get:

x = 7500 - 2 (1875)

x = 7,031,250 m^2

First let's find out what would the sides of a square be.

7500 / 4 = 1875

Now we have 1875 as the sides and double at the top.

So 1875 * 3750 = 7031250 meters squared