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1993 AMC 12 #13 - Square in a Square

Source:

January 2, 2012
geometryperimeterAMC

Problem Statement

A square of perimeter 2020 is inscribed in a square of perimeter 2828. What is the greatest distance between a vertex of the inner square and a vertex of the outer square?
<spanclass=′latex−bold′>(A)</span> 58<spanclass=′latex−bold′>(B)</span> 752<spanclass=′latex−bold′>(C)</span> 8<spanclass=′latex−bold′>(D)</span> 65<spanclass=′latex−bold′>(E)</span> 53 <span class='latex-bold'>(A)</span>\ \sqrt{58} \qquad<span class='latex-bold'>(B)</span>\ \frac{7\sqrt{5}}{2} \qquad<span class='latex-bold'>(C)</span>\ 8 \qquad<span class='latex-bold'>(D)</span>\ \sqrt{65} \qquad<span class='latex-bold'>(E)</span>\ 5\sqrt{3}
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