Help, math homework X_X

Dear 4chan math gurus,
I'm stuck on this math problem in my precalc book.  I'm hoping someone here could tell me how to solve it.  I already know the answer, I just need to know it's solved.  Here it is:

"A rectangular playground is to be fenced off and divided in two by another fence parallel to one side of the playground.  Six hundred feet of fencing is used.  Find the dimensions of the playground that maximize the total enclosed area.  What is the maximum area?"

Answer: 150 by 100 ft.  Total of 15000 ft^2

The last time I had a problem like this, I followed a model like this:

Perimeter = 3x + 2y
Area = xy

P = 600 = 3x + 2y
2y = 600 - 3x
y = (600 - 3x)/2
A = xy
A = x[(600 - 3x)/2]

This is where I get stuck.  If anyone had a better method or could (preferably) show me how I can get the answer through something along the lines of the above method, then I'd really appreciate it.  Thanks in advance.

sage

bump

differentiate, set to zero, etc etc

but you're in precalc, so take your quadratic for area(which opens down), and find its vertex, which will also be its maximum.

>>4
i dont think they differentiate in pre-calc.

if you dont know how to take derivative and find max/min's then just do this instead.

A = x[(600 - 3x)/2]  
this is the equation of an inverted parabola, notice zeros are at x = 0, and x = 200. so we know that the maximum point of the parabola (hence the maximum area) occurs at x = 100.

then solve for y by plugging in x = 100 into y = (600 - 3x)/2

USE THE LAGRANGE MULTIPLIERRRRRRRRRRRRRRRRRRRRRRR

>>5
i might be stupid, but it looks like theres no other way to solve this (without a calculator) except for differentiation. sucks how they kinda make you use one. i barely used mine during precal, well except for polar graphs lol

>>7

No, there is a way. Which >>5 used.

>>7
Excuse me bro, but >>5 didn't use differentiation, he showed you how to find the max and min without using differentiation, thus demonstrating that the max area will be obtained with x = 100.

>>9
?  that's what he said too