Centroid of an isoceles triangle

[Zack K]

Homework Statement

Where is the center of mass of an isoceles triangle?

Homework Equations

x_cm=∫xdV/V (where V is the volume of the triangle)

The Attempt at a Solution

The representation of the sides is what I'm confused with. Flipping the triangle to it's side is what's recommended to be able to express it better. Taking a small chunk and labeling it's side, you can express the length of this chunk to be 2y(replacing y with b(the base)). My issue is what should I label the shorter side as? Should I label it as x, another variable, or in terms of y?

 

[kuruman]

You are not describing very well your difficulty with this. An isosceles triangle needs two numbers to be defined. Common choices are the base $b$ and the the two equal sides $a$ or the base $b$ and the two equal angles $\theta$, or the base $b$ and the height $h$. You can choose any two symbols to label these. Personally, I would choose the base and the height. Of course, to find the CM you need to integrate over variables so, to avoid confusion, it is a good idea to reserve $x$ and $y$ as the names of the integration variables. So pick a scheme, and then explain what your difficulty is. Providing a drawing would be a nice touch.