Area of Triangle formed by Centers of Faces
Source: 2013 AIME I Problem 7
March 15, 2013
geometryratiotrigonometryvectorquadraticsAMCAIME
Problem Statement
A rectangular box has width inches, length inches, and height inches, where and are relatively prime positive integers. Three faces of the box meet at a corner of the box. The center points of those three faces are the vertices of a triangle with an area of square inches. Find .