Answer:
Step-by-step explanation:
Centroid of a triangles is a point of intersection of it's medians.
Centroid divides the medians in the ratio of 2 : 1.
By this property of the centroid,
SH : HM = 2 : 1
Since, SM = 24,
SH = [tex](\frac{2}{2+1})(SM)[/tex]
= [tex]\frac{2}{3}\times 24[/tex]
SH = 16
HM = SM - SH
= 24 - 16
HM = 8
TH : DH = 2 : 1
Since, DH = [tex](\frac{1}{2+1})(TD)[/tex] = 4
[tex]\frac{1}{3}(TD) = 4[/tex]
TD = 12
Therefore, TH = TD - DH
= 12 - 4
TH = 8
Since, EH = [tex](\frac{1}{2+1})(ER)[/tex] = 6
[tex]\frac{1}{3}(ER)=6[/tex]
ER = 18
Therefore, HR = ER - EH
= 18 - 6
HR = 12
