Question 737525


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+5}}} and {{{BP=7x+4}}}, then {{{2PM=BP}}} 

{{{2(2x+5)=7x+4}}}......solve for {{{x}}}

{{{4x+10=7x+4}}}

{{{10-4=7x-4x}}}

{{{6=3x}}}

{{{6/3=x}}}

{{{2=x}}}

so, the length of {{{PM}}} will be

{{{PM=2*2+5}}}
{{{PM=4+5}}}
{{{highlight(PM=9)}}}

and

{{{BP=7*2+4}}}

{{{BP=14+4}}}

{{{BP=18}}}