Question

Please solve and answer this

Answer 1

given, DE = FE, so,
triangle DEF is isoceles,

as the perpendicular line EH divides this triangle into 2 congruent parts,
 and EH is also the median,
                   
                   DH = FH = 9 (given)

Now, as the centroid divides the median into 2 : 1 ratio,

                      2/1 = EP/PH = 8/PH
                      PH = 8/2 = 4.
Then as EH = EP + PH, EH = 8 + 4 = 12.

Thank you.