Problem Set 2
Recall that the Pythagorean Theorem is that the sum of the squares of the two legs of a right triangles is equal to the square of the hypotenuse, or for legs, a and b, and hypotenuse, c, of some right triangle. Explore this idea in two dimensions.
1. Use the Pythagorean Theorem to find the hypotenuse for the following set of legs, and show that it works, geometrically.
a) 3 and 4 b) 5 and 12 c) 7 and 24 d) 8 and 8
Geogebra Applet for Problem 1
2. Find another pythagorean triple based off one of the above right triangles. Show that it is a Pythagorean Triple.
Geogebra Applet for Problem 2
3. Is there a way to calculate a pythagorean triple?
a) For x = 7, find and . Check to see if these three values make a right triangle. b) For x = 8, find and . Check to see if these three values make a right triangle. c) Do you have any conjectures? Test it. Prove it. This problem was “brought” to you by Plato (plus.math.org).