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Medians $\overline{DP}$ and $\overline{EQ}$ of $\triangle DEF$ are perpendicular. If $DP= 18$ and $EQ = 24$, then what is ${DE}$

 Feb 24, 2020
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The formulas for the medians are

AA' = 1/2*sqrt(2*AB^2 + 2*AC^2 - BC^2),

BB' = 1/2*sqrt(2*AB^2 + 2*AB^2 - AC^2),

CC' = 1/2*sqrt(2*AC^2 + 2*BC^2 - AB^2).

 

Using these formulas, and Pythagoras, we can prove that DE = 8*sqrt(2).

 Feb 24, 2020

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