Sunday Times Teaser 3017 – Mr Green’s Scalene Mean Machine
by Stephen Hogg
Published Sunday July 19 2020 (link)
My maths teacher, Mr. Green, stated that the average of the squares of any two different odd numbers gives the hypotenuse of a right-angled triangle that can have whole-number unequal sides, and he told us how to work out those sides.
I used my two sisters’ ages (different odd prime numbers) to work out such a triangle, then did the same with my two brothers’ ages (also different odd prime numbers). Curiously, both triangles had the same three-figure palindromic hypotenuse. However, just one of the triangles was very nearly a 45° right-angled triangle (having a relative difference between the adjacent side lengths of less than 2%).
In ascending order, what were my siblings’ ages?