Question

Find the measure of
SH
HM
TH
HR
TD
ER

Answer 1

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 =
`((2)/(2+1))(SM)`

=
`(2)/(3)* 24`

SH = 16

HM = SM - SH

= 24 - 16

HM = 8

TH : DH = 2 : 1

Since, DH =
`((1)/(2+1))(TD)` = 4

`(1)/(3)(TD) = 4`

TD = 12

Therefore, TH = TD - DH

= 12 - 4

TH = 8

Since, EH =
`((1)/(2+1))(ER)` = 6

`(1)/(3)(ER)=6`

ER = 18

Therefore, HR = ER - EH

= 18 - 6

HR = 12