SOLUTION: In the diagram below, point P is the centroid of ΔABC. http://imageshack.us/photo/my-images/441/centriod.png/ If PM=2x+5 and BP=7x+4, what is the length of PM?

Algebra ->  Triangles -> SOLUTION: In the diagram below, point P is the centroid of ΔABC. http://imageshack.us/photo/my-images/441/centriod.png/ If PM=2x+5 and BP=7x+4, what is the length of PM?      Log On


   

Question 737525: In the diagram below, point P is the centroid of ΔABC.
http://imageshack.us/photo/my-images/441/centriod.png/
If PM=2x+5 and BP=7x+4, what is the length of PM?
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

A fascinating fact is that the centroid is the point where the triangle's medians intersect, and the centroid is exactly two-thirds the way along each median.
If PM=2x%2B5 and BP=7x%2B4, then 2PM=BP
2%282x%2B5%29=7x%2B4......solve for x
4x%2B10=7x%2B4
10-4=7x-4x
6=3x
6%2F3=x
2=x
so, the length of PM will be
PM=2%2A2%2B5
PM=4%2B5
highlight%28PM=9%29
and
BP=7%2A2%2B4
BP=14%2B4
BP=18