quadratic application

[waterbottlee]

A rectangular enclosure is made with 120 ft of fencing on three
sides. The fourth side is the wall of the barn. Find the greatest
possible area of such an enclosure.

hi!

can anybody give me a hint on how to start..?i am confused on how to write the equation..

[OfficeShredder]

Your fenced off area is going to look like this:



x
------------------
|
|
|
| y
|
|
-------------------
x

where the right side of the area is the barn (so we don't need to worry about how long it is, though the length is clearly y).

So you have two equations:

2x + y = 120
xy = A

And you want to maximize A

[waterbottlee]

thank you..i found a way to do it by graphing and finding the vertex

[OfficeShredder]

That would exactly be the correct method. If you've taken calculus, you'll notice that just taking the derivative for A and solving for when it equals zero is equivalent, but probably a bit faster

[HallsofIvy]

You could also find the vertex by completing the square. That has the advantage of giving the exact answer while graphing can only give an approximate answer. (Of course, with a "made up" problem where you can rely on the answers being nice, integer values, that's not a problem!)