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.
+128474 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
