AoPS Wiki talk:Problem of the Day/September 12, 2011

Revision as of 15:37, 12 September 2011 by Negativebplusorminus (talk | contribs) (Created page with "Dropping an altitude, we see that it has length <math>3\sqrt{2}</math> by the 45-45-90 triangle. Thus, the midsegment must have length <math>5\sqrt{2}</math>. Dropping altitude...")
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Dropping an altitude, we see that it has length $3\sqrt{2}$ by the 45-45-90 triangle. Thus, the midsegment must have length $5\sqrt{2}$. Dropping altitudes from B and C, we see that the sum of the bases is $2BC+6\sqrt{2}$, and thus $BC+3\sqrt{2}=5\sqrt{2}$ and $\boxed{BC=2\sqrt{2}}$.