Question

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

Answer 1

Explanation:

Answer 2

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=(1)/(3)*FQ=(1)/(3)*24=8`
Also,

`x=(2)/(3)* DP=(2)/(3)* 18=12`
Since the medians are perpendicular, we deduce that:

`x^2+y^2=DQ^2\iff DQ=√(8^2+12^2)=14.4`
Then, since
`DE=2* DQ\text{ then }DE=2* 14.4=28.8`