In ACE,G is the centroid and BE = 15. BE is a median.Find BG and GE
In triangle ACE, BE is a median, which means that it divides AC into two equal segments. Therefore, AE = CE.
Since G is the centroid, it divides the median BE into two segments in a 2:1 ratio. Let's denote BG as x and GE as y.
Thus, we have the following equation:
BG/GE = 2/1
Substituting the value of BE (which is 15) into the equation, we get:
x/y = 2/1
x = 2y
Since AE = CE, the total length of AC is 2AE or 2CE. Therefore, AC = 2(AE) = 2(CE).
Since G is the centroid, AG = CG = 2/3 of AE or CE, and BG = GE = 1/3 of AE or CE.
Knowing that AE = CE and BG = GE, we can equate the lengths as follows:
BG = GE
2y = y
y = 15/3
y = 5
Thus, GE = 5.
Using the equation x = 2y, we can calculate BG:
BG = 2(5)
BG = 10
Therefore, BG = 10 and GE = 5.