Question

Given this super-sized board (16x16), what integer lengths are possible for slanted segments? Use the line tool to sketch them (using a different color for each one). Label each length. Then describe how you found them.

Answer 1

A way to find integer line segments is using Pythagorean triples, that is, positive integers that are consistent with the Pythagorean theorem, for example, (3,4,5) because we have

`3^{2^{}}+4^2=5^{2^{}}`

therefore, they can be put in a triangle like this

Therefore, the slanted segment would have a length of 5. That can be done with other Pythagorian triples like (5,12,13) or (8,15,17).