+29 In triangle ABC, D is the altitude from A to BC, E is the altitude from B to AC, and F is the altitude from C to AB. H is the point where all three altitudes intersect. We know that:
BD = CD
HD = 5
AH = 11
Find the area of triangle ABC.
+129771 Triangle BDH similar to triangle BEC
BD/ DH = BE /EC
BD / 5 = BE / EC
BD * EC / 5 = BE
Triangle BEC similar to triangle ADC
BE / EC = AD / DC
BE / EC = 16 / DC
BE / EC = 16/ BD
BE = 16EC / BD
BD * EC / 5 = 16 EC / BD
BD ^2 = 80
BD = 4 sqrt 5
[ABC ] = BD * AD = (4sqrt 5) * 16 = 64 sqrt 5 ≈ 143.1
CORRECTED !!!
+29 I think you made an error... BD^2 = 80, not 16/5. You divided by 5, not multiplied it. But thank you!
