Slice off the corner of a right rectangular prism so that the result is a tetrahedron with three right triangular faces mutually perpendicular to each other. The fourth face is a triangle formed by the hypotenuses.
Prove: The sum of the squares of the areas of the three right triangles is equal to the square of the area of the fourth.
(In reply to Cutting Corners?
It's hard to tell. You ask for a relation between integer side lengths and a formula. You don't specifically ask for the relation between the areas in general terms, except in your official solution and your reply 'Explanations anyone?'
It seems like maybe you are trying to get people to derive the theorem without knowing it, whereas I give the theorem and ask for a proof.
I think the two problems go well together.
Posted by Jer
on 2017-06-17 10:34:23