SOLUTION: A rectangular piece of land, bounded on one side by a river, is to be fenced on the other three sides. What is the largest possible area that can be enclosed by 300 meters of fenci

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: A rectangular piece of land, bounded on one side by a river, is to be fenced on the other three sides. What is the largest possible area that can be enclosed by 300 meters of fenci      Log On


   

Question 764039: A rectangular piece of land, bounded on one side by a river, is to be fenced on the other three sides. What is the largest possible area that can be enclosed by 300 meters of fencing? Complete the square to find the maximum area.
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
One side would be 300-x and the other side side lengths are each x. The area in general is a function of x.
A%28x%29=x%28300-x%29 and the length of fencing is 300.

We can use the function in factored form to find the zeros. The x value in exactly the middle of the zeros is that at which A is either a minimum or a maximum. Here, we can see that A(x) is -x%5E2%2B300, which is a parabola with a maximum, seeing that the coefficient on x^2 term is -1.

With that, can you find the maximum area?
(BIG HINT: A=0 when x=0 or x=300)