Question

A cardboard sheet is cut in the shape of a triangle, with vertices at (0,0), (20,0), and (3,4) units. the thickness of the sheet is uniform. what is the x-coordinate of its center of mass?

Answer 1

This problem can be solved in two ways, the long way, or the short way.

1. The long way
We know that the base of the triangle is along the x-axis, and the length of the base is 20.
The centre of mass is located at 2/3 of the distance from vertex (3,4) along the median, which cuts the base at (10,0).
Therefore the centre of mass is located at
x=3+(10-3)*2/3=23/3
y=4/3

2. The short way
It turns out that the centre of mass of a triangle sheet is located at the mean of the coordinates of the three vertices, i.e.
CG=((0+20+3)/3, (0+0+4)/3)=(23/3, 4/3)  as before.