Question

It is believed that surveyors in ancient Egypt laid out right angles using a rope that they bent into the shape of a triangle. The rope had eleven equally spaced knots along its length that divided the rope into twelve sections. What Pythagorean Triple could the surveyors use this rope to make?

1. 8, 15, 17
2. 12, 5, 13
3. 12, 35, 37
4. 3, 4, 5

-----HELP ME! : /

Answer 1

So the rope is one length divided into 12 sections right? If it were straight it would look something like ____________, where the spaces are the knots right? The question says that they bent the rope to the shape of a triangle, so all of the lengths have to add up to 12, because that is all they had to work with in that case. The only one of those options given that add up to equal 12, is 3, 4 , 5. And think if you took 3 knot spaces ---- and bent it at the fifth, you would have 8 sections going upward, then if you took three sections ---, you would only have 5 more sections left, but just enouh to make a full right triangle. Otherwise you would have too much length or not enough. It would not be a perfect triangle plus all of the other options gives you nothing sensible anyway. Let me know if you have any questions.