Posted by Kara on Monday, November 12, 2012 at 9:40am.
A dog trainer has 64 ft of fencing that will be used to create a rectangular work area for dogs. If the trainer wants to enclose an area of 192 ft2, what will be the dimensions of the work area?

Algebra  Steve, Monday, November 12, 2012 at 10:07am
guessing way:
192 = 2^6*3 = 16*12 = 8*24
2(8+24) = 64
so the work area is 8x24
algebraic way:
If the pen's width is w, then the length is 32w
w(32w) = 192
w^2  32w + 192 = 0
(w8)(w24) = 0
w = 8 or 24
so, the pen is 8x24
Unless you use the quadratic formula, factoring the polynomial is essentially the same as guessing the right factors of 192!
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