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Question: draw a right triangle whose legs are 2 cm and...

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Draw a right triangle whose legs are 2 cm and 1 cm long. Use the hypotenuse of this right triangle as one of the legs of a second right triangle, and construct the other leg so that it is 2 cm long and adjacent to the previous 2-cm leg, as shown below.
2 2

  1. If continuing this process infinitely, find a general mathematical rule for the number of triangles needed to produce a rational hypotenuse.

  2. Consider a similar situation where your original right triangle has leg lengths of 3 cm and 4 cm respectively. Assume that you build right triangles adjacent to this original right triangle with a leg length of 4 cm indefinitely. Create a general mathematical rule (similar to question d) for the number of triangles needed to produce a rational hypotenuse.

AQ: Generalize your learning from the previous questions by producing a mathematical rule for the number of triangles needed if your original right triangle has leg lengths of a cm and b cm while each additional triangle has a leg length of a cm.

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