Question

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

Answer 1

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

Answer 2

Answer:

Step-by-step explanation: