"A rectangular pasture is subdivided into two equal pens. Using the barn as one side and 132 m of fencing for the rest, find the value of x that gives the maximum area, and A(x)."

It gives no diagram whatsoever, so I have no idea if all the sides are the same length or not, etc etc... Can someone show me how to work out this problem please? Any help is GREATLY appreciated!! :D

The fence will look like a letter E. The open end of the letter E is the face of the barn.

It does not matter which length x stands for, as long as the total length of the fence is 132 m.

Let x be one of the three equal sides, and the length of the barn fenced in is 132-3x.
Total area
A(x) = x(132-3x)
A'(x) = 132-6x =0
Therefore x=132/6=22 m
The area is x(132-3x)=22(66)=1452 m²
check: A"(x) = -6 <0, therefore maximum.

Ohhhh I totally get it now!!! Thanks! :D

Glad that it helped! :)

Sure! I can help you solve this problem step by step.

To find the value of x that gives the maximum area, we need to first understand the given information and formulate a mathematical representation of the problem.

From the problem description, we know that the rectangular pasture is divided into two equal pens. Since a rectangle has opposite sides equal in length, this implies that the two pens are congruent rectangles.

Let's assume that the width of each pen is x. Since the pasture is divided into two equal pens, the total width of the pasture will be 2x. The length of each pen will be the remaining length after subtracting the width.

Now, let's calculate the length of each pen. The total amount of fencing used is given as 132 m, and the barn is one side, which means the rest of the fencing will be used to enclose the two pens:

Total fencing used - length of the barn = 2(width of each pen) + 2(length of each pen)

132 - length of the barn = 2x + 2(length of each pen)

Since the length of each pen is the remaining length after subtracting the width, we can write:

132 - length of the barn = 2x + 2(132 - 2x)

Simplifying this equation, we get:

132 - length of the barn = 2x + 264 - 4x

Rearranging terms, we have:

length of the barn - 132 = -2x + 264

Now, we need to determine the length of the barn. Unfortunately, the problem does not provide this information directly. You mentioned that there is no diagram. Without the length of the barn or any other relevant details, it is not possible to calculate the value of x or the maximum area.

In math problems, it is essential to have all the necessary information and details to accurately solve the problem. Without this information, it is not possible to determine the value of x or find the maximum area.