MathDB

A cube with side length 10 is suspended above a plane. The vertex closest to the plane is labelled

A

. The three vertices adjacent to vertex

A

are at heights 10, 11, and 12 above the plane. The distance from vertex

A

to the plane can be expressed as

\tfrac{r-\sqrt{s}}{t}

, where

r

s

, and

t

are positive integers, and

r+s+t<1000

. Find

r+s+t

Problem Statement