Answer: a) [tex]\dfrac{13}{7}[/tex]
Step-by-step explanation:
Median: Line segment from one vertex of a triangle to the midpoint of the opposite side. i.e. it bisects the opposite side.
Centriod: Point of intersection of a triangle of its medians
.Also, it is [tex]\dfrac23[/tex] of the distance from vertex to the midpoint of opposite side.
Given: CD is a median in triangle ABC and M is centriod.
[tex]\Rightarrow CM=\dfrac23 CD[/tex]
Since CM = x +5 and CD = 5x + 1
[tex]\Rightarrow\ x+5=\dfrac{2}{3}(5x+1)\\\\\Rightarrow\ 3(x+5)=2(5x+1)\\\\\Rightarrow\ 3x+15=10x+2\\\\\Rightarrow\ 10x-3x=15-2\\\\\Rightarrow\ 7x=13\\\\\Rightarrow\ x=\dfrac{13}{7}[/tex]
Correct option is a)
