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?