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Medians in a Right Triangle

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June 13, 2009
Pythagorean Theoremgeometry

Problem Statement

AB‾ \overline{AB} is the hypotenuse of a right triangle ABC ABC. Median AD‾ \overline{AD} has length 7 7 and median BE‾ \overline{BE} has length 4 4. The length of AB‾ \overline{AB} is: <spanclass=′latex−bold′>(A)</span> 10<spanclass=′latex−bold′>(B)</span> 53<spanclass=′latex−bold′>(C)</span> 52<spanclass=′latex−bold′>(D)</span> 213<spanclass=′latex−bold′>(E)</span> 215 <span class='latex-bold'>(A)</span>\ 10\qquad <span class='latex-bold'>(B)</span>\ 5\sqrt{3}\qquad <span class='latex-bold'>(C)</span>\ 5\sqrt{2}\qquad <span class='latex-bold'>(D)</span>\ 2\sqrt{13}\qquad <span class='latex-bold'>(E)</span>\ 2\sqrt{15}
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