A farmer has 76 feet of fencing and he wants to build a rectangular pen for his chickens.what should the dimensions of the pen be if he wants it to have the greatest area possible

Question

anonymous · Answer

So the pen is a rectangle so it has 4 sides, right?. What I would do is divide 76 by 4 so that the length and width of the pen are equal. That gives you 19 for both width and length. You find the area of the pen by multiplying the width and length sooo

anonymous · Answer

Okay, let's call the length of the pen L and the width W.

2L + 2W = 76, because the total length of all four sides is equal to the amount of fencing the farmer has.

So L * W = a maximum.

Taking the first equation, we can find that L = (76 - 2W)/2, or L = 38 - W. Substituting that into the second equation, we get:

38W - W^2 = a maximum.

At this point, if you have a graphing calculator, one way to solve it is to enter 38x - x^2 as your equation, and use the calculator's function to look for a maximum. But I'm going to try and solve it without that.

anonymous · Answer

I wasn't sure if he was up to that stuff yet, lol. His question seemed a lot more simpler to me... More like a Guess-and-Check kind of thing.

anonymous · Answer

I think it'd be easy to solve with a guess and check method, too. Probably easier. 

So try guess and check, and if you need guidance, check the graph!

anonymous · Answer

More like 19 x 19, but yes.