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In triangle ABC, AB = 3, BC = 4, and AC = 5.  G is inside triangle ABC, so that the distance from G to BC is 1, and the distance from G to AC is 1/2.  Find the distance from G to AB.

 Dec 8, 2020
 #1
avatar+117546 
+2

Area of  right triangle   =(1/2)  (product of legs)  = (1/2) (3 * 4)  =  (1/2)(12)  =6

 

Area of  triangle   AGC  = (1/2) AC * GC  = (1/2) (5) (1/2)  = 5/4

 

Area of  triangle  BGC  =  (1/2) BC * GP  = (1/2) ( 4) (1)  = 2

 

Area of triangle  AGB =  6 - 5/4  - 2  =  4  - 5/4   =   11/4

 

Area of triangle AGB  = (1/2) AB * RG 

 

11/4 =  (1/2) 3 * RG

 

11/4 = 3/2 * RG

 

RG  = (11/4) (2/3)  =  22/12  =  11/6   =  distance  from G to AB

 

 

cool cool cool

 Dec 8, 2020
 #2
avatar+1164 
+1

Clever solution!!!

I was using trig to solve it.smiley

jugoslav  Dec 8, 2020
edited by jugoslav  Dec 8, 2020
 #3
avatar+117546 
0

Thx, jugoslav....!!!!

 

 

cool cool cool

CPhill  Dec 9, 2020

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