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
[tex]y=\frac{1}{3}\timesFQ=\frac{1}{3}\times24=8[/tex]
Also,
[tex]x=\frac{2}{3}\times DP=\frac{2}{3}\times 18=12[/tex]
Since the medians are perpendicular, we deduce that:
[tex]x^2+y^2=DQ^2\iff DQ=\sqrt{8^2+12^2}=14.4[/tex]
Then, since [tex]DE=2\times DQ\text{ then }DE=2\times 14.4=28.8[/tex]
