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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.

 Jun 4, 2024
 #1
avatar+129401 
+1

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  !!!

 

cool cool cool

 Jun 4, 2024
edited by CPhill  Jun 4, 2024
 #2
avatar+29 
+1

I think you made an error... BD^2 = 80, not 16/5. You divided by 5, not multiplied it. But thank you!

dplostthegame  Jun 4, 2024
 #3
avatar+129401 
0

Thanks for catching my error....corrected  !!!

 

cool cool cool

CPhill  Jun 4, 2024

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