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! :]
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:
