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How to Connect Three Squares to Form a Right Triangle

What do three squares have to do with a triangle? Ask Pythagoras, a philosopher and mathematician in Ancient Greece. If you understand some basic mathematical principles, you can create a right triangle by connecting three squares. The method involves making the sides of the squares the right length and using some creativity. You must be familiar with the Pythagorean theorem to complete the following steps.

Things You'll Need

Paper
Writing utensil
Ruler

Instructions

Calculate length of sides
- 1
  Apply the Pythagorean theorem to figure out the side lengths of your triangle (a^2 + b^2 = c^2). Suppose that the length of one of the triangle's sides is 3 inches. Substitute the a in your equation with 3. Your equation should now read 3^2 + b^2 = c^2.
- 2
  Find the length of the second side (not the hypotenuse) by substituting the b in your equation with 4. This will signify that this side's length equals 4 inches. Your equation should read 3^2 + 4^2 = c^2.
- 3
  Simplify your equation as follows:
  
  9 + 16 = c^2
  
  25 = c^2
- 4
  Solve for c^2 (the hypotenuse) by finding the square root of 25. Thus, 5 inches is the length of your right triangle's hypotenuse.
Creating squares
- 5
  Begin to build your squares now that you know the side lengths of your triangle equal 3, 4 and 5 inches. Because you know that all sides of a square are equal in length, you can extrapolate the size of your squares if you know the length of only one side.
- 6
  Take your paper and draw a 3-inch long line on it. Create a square with an area of 9 square inches by making all four sides of this triangle 3 inches long.
- 7
  Place your writing utensil at the top left corner of the 9 sq in square. Draw a vertical line 4 inches long up from that corner, so that it aligns with the left side of the 9 sq in square.
- 8
  Continue to draw a 16 sq in square by drawing a horizontal line going out 4 inches from the top left corner of the 9 sq in square, so that the bottom right corner of the new 16 sq in square touches the top left corner of the old 9 sq in square and creates four 90-degree angles. Close off the new square by drawing two more 4 inch sides.
- 9
  Draw a line from the top right corner of the first square to the top right corner of the second square. This line should be 5 inches long. Repeating the process for the other squares above, complete this 25 sq in square by drawing three more 5 inch sides that do not overlap with any other lines. These lines should jut out away from the right triangle that is now in the center of your three squares.

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