Question

A right triangle has legs of lengths q and r and hypotenuse of length s. Use the Pythagorean Theorem to write an expression for the length of the hypotenuse, s. Then, choose your own values for q and r so that s is a whole number. What is the value for s? Show your work.

Answer 1

`a^2 + b^2 = c^2\\\\q^2 + r^2 = s^2\\\\s = √(q^2+r^2)\\\\`

Through trial and error, q = 3 and r = 4 will lead to s being a whole number.

`s = √(3^2+4^2)\\\\s = √(9+16)\\\\s = √(25)\\\\s = 5\\\\`

This is a 3-4-5 right triangle. It's one of the infinitely many pythagorean triples.