Answer:
x = 5
OB = 36
BE = 54
Step-by-step explanation:
We know that the medians of the triangle divides in a ratio of 2:1. Therefore we have the equation:
[tex]\dfrac{9x-9}{2x+8}=\dfrac{2}{1}[/tex] cross multiply
[tex]1(9x-9)=2(2x+8)[/tex] use distributive property a(b + c) = ab + ac
[tex]9x-9=(2)(2x)+(2)(8)[/tex]
[tex]9x-9=4x+16[/tex] add 9 to both sides
[tex]9x=4x+25[/tex] subtract 4x from both sides
[tex]5x=25[/tex] divide both sides by 5
[tex]\boxed{x=5}[/tex]
[tex]OB=9x-9\to OB=9(5)-9=45-9=\boxed{36}[/tex]
[tex]OE=OB:2\to OE=36:2=18\to BE=BO+OE\to BE=36+18=54[/tex]
