Algebraic Polynomials
posted by Anonymous on .
I don't know where to go about creating a polynomial equations for the following problem: A piece of wire 52 in. long is cut into two pieces, and then each piece is formed into a square. If the sum of the areas of the two squares is 97 in.^2, how long are the pieces of wire? My attempted starting point is 97 = (1/4(x))^2 + ((1/4)(52x))^2, but my numbers don't seem to work. Help is appreciated!

Your equation is perfectly correct.
What did you get for solution? 
Once I move numbers around to achieve a trinomial, I have (1/8)x^2  (13/2)x + 72, I'm just not sure how I would factor that.

Expand
97 = (x/4)^2 + ((52x)/4)^2
to get
x^2/813x/2+72=0
multiply by 8 throughout to get
x^252x+576=0
factor and solve for x.
You should get two positive integers which add up to 52.