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Algebra 2: Quadratic Equations



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Wed Oct 27, 2010 10:27 pm
Joy Sauce says...



I'm stuck on a word problem, of course. It asks for the dimensions of a rectangle with a perimeter of 66 ft and an area of 216 ft^2. I did the math mentally and got that the sides are 9 and 24, but I must write and solve (using the zero-product property) a quadratic equation in order to get credit; I'm having trouble figuring that out. So, if it can be explained, thank you! :]
  





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Wed Oct 27, 2010 11:44 pm
Kale says...



Ah, don't you just love it when they require you to show your work? I feel your pain, my dear, and so here I am to help!

The quadratic equation would be:

x^2 - 33x + 216 = 0

33 comes from l*w since perimeter is 2lw.

The b term must be negative in order for the equation to equal 0.
- Think what would happen if everything was addition.
- Since we are talking side lengths, you can't have a negative length, so the first and third terms must be positive.

From there, it's just a matter of factoring and finding the zeros. You'll wind up with:

(x - 9)(x - 24) = 0

And so x = 9 and 24, which are your two sides.
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Thu Oct 28, 2010 12:08 am
Joy Sauce says...



Ah, yes, that makes sense now. =D Thank you so much!
  








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