SOLUTION: Hi, I really appreciate if you could help me with following math problem. Thanks!! A farmer has 216 feet of fencing and wants to build two identical pens for his price-winning

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Question 825456: Hi, I really appreciate if you could help me with following math problem. Thanks!!
A farmer has 216 feet of fencing and wants to build two identical pens for his price-winning pigs.The pens will be arranged as shown. Determine the dimensions of a pen that will maximize its area. The solution is given, it would be 27' x 36'.
[ | ] these two pens share 1 side, the middle one; x is the width and y represents the length.
I just can't figure out how to solve it.
I reckon that the perimeter 216= 3x+ 2y and the area A= x times 2y.
I figured out that in this case y= 108 - (3x/2).
-> A= 2*(108- (3x/2)* x
= (216-3x)*x
= 3x^2-216x
= 3 (x^2 - 72x )
= 3 (x^2 -72x + 1296) -1296
= 3 (x-36)^2 -1296 (which I though is the product maximum)
36 is one factor of 1296 and as I know one of the solutions. Therefore 27 should be the other solution but it cannot multiply with 36 to a product of 1296. That is why I'm superconfused. Please help me as quickly as possible. Thanks in advanced.
Answer by josgarithmetic(39618) (Show Source):
You can put this solution on YOUR website!
The picture or diagram is not shown to us, but your fencing formula which I would not really call as "perimeter", is correct, indicating that x is one of the lengths of the divider as well as one of the dimensions of the whole rectangular form. y is the other dimension of the whole rectangular form.

Your mistake only appears to be your area formulation. This should be, ;

From this, you may find no further trouble nor confusion.