Farmer ed has 7000 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 are that can be enclosed?

Let

x--------> the length side of the rectangular plot (assume side along the river)

y------> the width side of the rectangular plot

we know that

the perimeter of the rectangular plot is equal to

so

Clear variable y

-------> equation

The area of the rectangular plot is

------> equation

substitute equation in equation

we know that

To find the larger area that can be enclosed------> Find the vertex of the quadratic equation

The quadratic equation is a vertical parabola open down

so

the vertex is a maximum

using a graphing tool

see the attached figure

the vertex is the point

that means

For

the largest area is

Find the value of y

the dimensions of the rectangular plot are

therefore

the answer is

The largest area that can be enclosed is

your answer would be 12