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

Question

vredina

11 days ago

13

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

?

Mathematics

2 answers:

zzz [12.3K] · Answer 1 · 2026-04-05T12:42:05+03:00

Let M represent the intersection point of the medians.
Assign the distance from D to M as x and from Q to M as y.
Based on the properties of triangle medians, we understand that
$y=\frac{1}{3}\timesFQ=\frac{1}{3}\times24=8$
Furthermore,
$x=\frac{2}{3}\times DP=\frac{2}{3}\times 18=12$
Recognizing that the medians are perpendicular permits us to deduce that:
$x^2+y^2=DQ^2\iff DQ=\sqrt{8^2+12^2}=14.4$
Thus, since $DE=2\times DQ\text{ then }DE=2\times 14.4=28.8$

Inessa [12.5K] · Answer 2 · 2026-04-05T12:39:37+03:00

Inessa [12.5K]11 days ago

3 0

Result:

Detailed explanation: