Square Puzzle - Green

Directions: Use the five puzzle pieces to make a square. Different sizes of squares can be made with some or all of the pieces. However, there is a square that can be made with all five pieces. When I carefully cut them out, I was able to put them together so that I had no more than one millimeter of error between any of the pieces.

Hint: If you tried to make the square, you probably made a square with four of the pieces and had one piece left over. That means that the size of the square made from four pieces with one piece left is smaller (length and area), than the square that can be made with the five pieces.

Okay, I agree that is obvious when you think about it, but look at the pieces that were used to make that square. I bet that the longest side of any piece in the four piece square was positioned so that the longest side was an edge of the square.

Flash of enlightenment? If there is not one side of any piece that is long enough to make a square big enough (in area) for all five pieces, then every side of the five piece square must have more than one side of each piece for every side of the square.

Wow! Is that counter intuitive or what? I thought otherwise too. So think about what else could be done with the longer sides.

Math stars: Label one of the sides X and figure what the relationship of X is to all the other sides. If you do you'll have a new respect for squares and square roots.

Wow!

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