If x ft. of stonewall is used as one side of the field, express the area enclosed as a function of x according to the problem below.A farmer has...

Since the field is rectangular, we'll establish the
dimensions length and width as x and y.

Now, we know, from
enunciation that there are available 600 ft wire to enclose the field and to build more
wire walls, namely 2 inner walls, parallel to the stone
wall.

So, the total amount of 600 ft could be expressed
as:

3x + 2y = 600 (1)

We did
not put 4x because one wall is made of stone and we did not put 2x because we have 2
more inner wire walls, besides the end wall.

To calculate y
with respect to x, we'll subtract 3x both sides, in (1).

2y
= 600 - 3x

We'll divide by
2:

y = 300 - 3x/2 (2)

Now,
we'll express the area enclosed:

A =
length*width

A = x*y

We'll
substitute y by (2):

A = x*(300 -
3x/2)

We'll remove the brackets and we'll
have:

A = -3x^2/2 + 300x