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

###### Question details

Introduction: 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. Find the length of the hypotenuse of the second right triangle.

Use this hypotenuse as one of the legs of a third right triangle, and construct the other leg so that it is 2 cm long and adjacent to the previous 2-cm leg. Find the hypotenuse of this right triangle.

If you were to continue this process, after how many triangles would you have the next rational hypotenuse length?

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

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.