Pre calculus question

Question

A farmer wants to build a rectangular pen for his cow, he wants to build his pen along a river so he will only need to have fence along 3 of the sides. He has 1000 ft of fencing, what should the dimensions be to maximize the area?

I have 3 answers for the area being:

1.125,000

2.62,500

3.375,000

Answer 1

For these types of problems, it's always best to draw diagrams to see what you're trying to do. I'm not going to give you the answer, but offer subtle hints.

But anyway, first come up with the equation of the perimeter of the rectangular fencing. Hint....two opposite sides are equal in length.

Next come up with equation of the total area....For example A=ab.

Substitute the a or b in the Area equation with the corresponding value in terms of the other variable. use distributive property to find the Area in terms of the one variable.

Find derivative of A in terms of that variable.

Set derivative =0, and solve for that variable. You can determine the values of the other variables once known. Multiply the lengths of one side to the length of the adjacent side to get the area.

This should be enough to start on. Giving you the solution without you doing some work would not help you in the long run.