Finding Center of Mass of 800g Steel Plate Triangle

[Anthonyphy2013]

Homework Statement

An 800 g steel plate has the shape of the isosceles triangle shown in the figure. What are the x and y coordinates of the center of mass?
https://www.physicsforums.com/attachment.php?attachmentid=13559&d=1208292919

Homework Equations

x=1/M ∫ x dm

3. The Attempt at a Solution [/b
I have no idea how to start the question

 

[SteamKing]

The image gives you a big ole hairy HINT. Did you try following it?

 

[Anthonyphy2013]

The image gives you a big ole hairy HINT. Did you try following it?

what hint is that ? the triangle is a smmetry and I put xcm=1/M∫xd(ρ/AH)
and the height is y=2/3 x as =mx+C. and should I put h = 2/3 x ?

 

[haruspex]

xcm=1/M∫xd(ρ/AH)
and the height is y=2/3 x as =mx+C. and should I put h = 2/3 x ?

That's a pretty confusing mix of variable names. What's AH, C, the m in mx+C? Why switch from y to h?
That said, y (=h) = 2x/3 looks right. What do you get for the integral?

 

[Anthonyphy2013]

xcm=1/M∫xd(ρ/AH) , A is the area and H is the height , I need to find h and I use h=mx+c to find the height and the slope is 2/3 . Question is to find the center of mass and only this integration could help me find the answer .

 

[haruspex]

xcm=1/M∫xd(ρ/AH) , A is the area and H is the height

ρ/AH is not going to give you mass. And... the area and height of what, exactly?
You want the mass, dm, of an element of width dx and height y = 2x/3. It's a 2-dimensional lamina, so the density is mass/area. So what is dm equal to?

 

[SteamKing]

More importantly, you have a plate with a simple shape composed of a material which has a constant density. Do you really need an integral to determine the location of the centroid?