Question

If the figure below, P is the centroid of triangle DEF, EH is Perpendicular to DF. If DH= 9cm, DG= 7.5 cm, EP= 8cm, and DE=FE. Find the lenth of FH, EH, PH and the perimeter of triangle DEF.

Answer 1

Please refer to the given figure:-
Since, DE = EF
ΔDEF is an isosceles triangle.
∴ EH ⊥ DF
DH = FH = 9 cm
FH = 9 cm
Since G is midpoint of DE
2DG = DE
DE = 2×7.5 = 15cm
By Pythagoras theorem,
h² = p² + b²
DE² = EH² + DH²
EH² = 15² - 9²
EH² = 225 - 81
EH² = 144
EH = 12cm
EH = EP + PH
PH = EH - EP
PH = 12-8
PH = 4cm
Perimeter of ΔDEF = DE + EF + DF
= 15 + 15 + 18
= 48 cm