Posted by **Anonymous** on Wednesday, March 28, 2012 at 8:38pm.

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)(52-x))^2, but my numbers don't seem to work. Help is appreciated!

- Algebraic Polynomials -
**MathMate**, Wednesday, March 28, 2012 at 11:48pm
Your equation is perfectly correct.

What did you get for solution?

- Algebraic Polynomials -
**Anonymous**, Thursday, March 29, 2012 at 2:31am
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.

- Algebraic Polynomials -
**MathMate**, Thursday, March 29, 2012 at 7:50am
Expand

97 = (x/4)^2 + ((52-x)/4)^2

to get

x^2/8-13x/2+72=0

multiply by 8 throughout to get

x^2-52x+576=0

factor and solve for x.

You should get two positive integers which add up to 52.

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