MathDB
Rectangular Box

Source: 2014 AMC 12B #14

February 20, 2014
geometryAMC

Problem Statement

A rectangular box has a total surface area of 9494 square inches. The sum of the lengths of all its edges is 4848 inches. What is the sum of the lengths in inches of all of its interior diagonals?
<spanclass=′latex−bold′>(A)</span> 83<spanclass=′latex−bold′>(B)</span> 102<spanclass=′latex−bold′>(C)</span> 163<spanclass=′latex−bold′>(D)</span> 202<spanclass=′latex−bold′>(E)</span> 402{ <span class='latex-bold'>(A)</span>\ 8\sqrt{3}\qquad<span class='latex-bold'>(B)</span>\ 10\sqrt{2}\qquad<span class='latex-bold'>(C)</span>\ 16\sqrt{3}\qquad<span class='latex-bold'>(D)</span>}\ 20\sqrt{2}\qquad<span class='latex-bold'>(E)</span>\ 40\sqrt{2}
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