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A rectangular playground is to be fenced off and divided into two parts by a fence parallel to one side of the playground. 360 feet of fencing is used. Find the dimensions of the playground that will enclose the greatest total area.
Uh hi. I guess if you're asking for help with homework or something? I can't help you :V But I'm just making sure so that other people know, people who can help you.
it'll be a 60 x 90 playground.
I'll scan in my (dad's) work later
EDIT: Alright, after talking to my dad today, we were able to come up with two ways to solve this problem. His way is with calculus; derivatives and whatnot. It's with the dA/dy stuff. I solved the problem by solving for the square.
Anyways, we found two equations because this is a two-variable question. Since the total fencing required is 360 ft., and there's a wall down the middle of it, and if x is the width of the playground and y is the length, then we get the equation 3x+2y=360. Then we find the area, which turns out to be xy. Then you use substitution in the first equation, so that you end up withs something like (360-3x)/2=y.
So then you plug that in to the second equation, so that A=x((360-3x)/2). Simplify that so that you end up with 180x-3/2x^2.
This is where my dad and I split, and I'll let you try to figure out what we did from the scan. :3
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