Math CentralQuandaries & Queries


Question from Susan, a parent:

If you have a piece of string 8 inches long and cut it in two pieces. Then take the pieces and forms
each into a square such that the area of each squares added together equals 2. How long are the
sides of the squares?

My son is doing quadratic equations and is supposed to set up a solution to solve it,
any help would be appreciated.

Hi Susan,

You want to cut the string but you don't know the lengths of the two pieces freer the cut. Suppose that the length of one of the pieces is x inches then the length of the other piece must be 8 - x inches. You now want to form two squares. Start with the piece of length x inches. If this length is the perimeter of a square then each side of the square is x/4 inches long. The area of this square is then (x/4)2 = x2/16 square inches.

What is the area of a square with perimeter 8 - x inches? The sum of the two areas is 2 square inches. Solve for x.


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