MathDB
External Diagonals

Source: 1993 AMC 12 #29

January 3, 2012
geometry3D geometryprismanalytic geometryinequalitiestrigonometrytriangle inequality

Problem Statement

Which of the following sets could NOT be the lengths of the external diagonals of a right rectangular prism [a "box"]? (An external diagonal is a diagonal of one of the rectangular faces of the box.)
<spanclass=latexbold>(A)</span> {4,5,6}<spanclass=latexbold>(B)</span> {4,5,7}<spanclass=latexbold>(C)</span> {4,6,7}<spanclass=latexbold>(D)</span> {5,6,7}<spanclass=latexbold>(E)</span> {5,7,8} <span class='latex-bold'>(A)</span>\ \{4, 5, 6\} \qquad<span class='latex-bold'>(B)</span>\ \{4, 5, 7\} \qquad<span class='latex-bold'>(C)</span>\ \{4, 6, 7\} \qquad<span class='latex-bold'>(D)</span>\ \{5, 6, 7\} \qquad<span class='latex-bold'>(E)</span>\ \{5, 7, 8\}