Question

In the figure below, ⎯⎯⎯⎯⎯⎯⎯⎯,⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯,

B
L
¯
,
A
M
¯
,
and ⎯⎯⎯⎯⎯⎯⎯⎯⎯
C
K
¯
are medians of △
△
A
B
C
. If KC = 108 and OC = 2n+10, then n=

Answer 1

Answer: n = 31

Step-by-step explanation:

The medians intersect at the centroid. This is one of the many centers of a triangle.

The centroid sub-divides the median KC such that segment OC is twice as long as segment KO.

This means that OC is 2/3 as long as KC.

OC = (2/3)*KC

2n+10 = (2/3)*108

2n+10 = 72

2n = 72-10

2n = 62

n = 62/2

n = 31