Medians $\overline{dp}$ and $\overline{eq}$ of $\triangle def$ are perpendicular. if $dp= 18$ and $eq = 24$, then what is ${de}$?

Denote by M the point of  intersection of the medians. 
Denote also the distance DM by x and the distance QM by y. 
From the median properties of triangles we know that
 
Also, 

Since the medians are perpendicular, we deduce that:

Then, since 

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