Question

Can someone please tell me how to solve this, I cant really understand

A farmer wishes to enclose a pasture that is bordered on one side by a river (so one of the four sides won't require fencing). She has decided to create a rectangular shape for the area, and will use barbed wire to create the enclosure. There are 600 feet of wire available for this project, and she will use all the wire. What is the maximum area that can be enclosed by the fence? (Hint: Use this information to create a quadratic function for the area enclosed by the fence, then find the maximum of the function.)

Answer 1

Explanation:

The maximum area that can be enclosed by the fence is 45000 square feet, the sides are 150 and 300, 150x300=45000

Answer 2

She only needs 3 sides take half for the side opposite the river, and divide the remaining part in to two for the other two sides, now we can do the work, but if you have to do more than one of these, a rectangle where one side is free (against a river, a side of a barn, whatever) half is for opposite side, the rest split in two gives other two sides if we put say y as the side opposite the river, and x as the adjacent sides, then you are told that x+x+y=600 i.e. 2x+y=600 the area is A=xy and you want it to be as large as possible solve for y and get y=600−2x then A(x)=x(600−2x)=600x−2x2 and base on that the answer would be 45000