Answer:
So the value of 'PU' is [tex]19[/tex]
Step-by-step explanation:
Given,
'p' is the centroid of [tex]\bigtriangleup XYZ[/tex] and [tex]XU=57[/tex]
∵ 'p' is the centroid then 'U' , 'V' and 'W' are the mid point of side 'YZ' , 'XZ' and 'XY'.
From Centroid Theorem we can write;
[tex]XP=\frac{2}{3} \times XU[/tex]
Plug the values 'XU' in above equation;
[tex]XP=\frac{2}{3} \times57[/tex]
[tex]XP=2\times 19[/tex]
[tex]XP=38[/tex]
From figure;
[tex]XP+PU=XU[/tex]
[tex]PU=XU-XP[/tex]
Plug 'XU' and 'XP' values;
[tex]PU=57-38[/tex]
[tex]PU=19[/tex]
∴ The value of 'PU' is [tex]19[/tex]
