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In the figure below, BL, AM, and CK are medians of △ABC. If KC = 108 and OC = 2n + 10, then n=
The picture is attached below.
The value of n is 31.
The median is the line connecting the vertex and its midpoint on the opposite side of the triangle.
The intersection of all 3 medians of the triangle is called the centroid.
As we know centroid divides the median in the ratio of 2:1.
In the given picture,
Medians of triangle △ABC are AM, BL, and CK.
So the centroid of the triangle is O.
Given that KC= 108
As the centroid O divides the line KC in 2:1.
Let OC=2x
KO= X
As KC= KO+OC
⇒ 108= x+2x
⇒ 3x=108
⇒ x=108/3
⇒ x=36
Then OC= 2x= 2*36= 72
As given in the question OC= 2n+10
putting the value of OC in above equation
⇒ 72= 2n+10
⇒ 2n= 72-10
⇒ 2n=62
⇒ n=62/2
⇒n=31
Therefore the value of n is 31.
Learn more about the median of the triangle
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