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the medians are divided by the centroid into the ratio of 2/3 to 1/3

So they are equal, I'm thinking..

Oh, I think I get it now.. so it's 2(20)-3

oh okay, now I think it is 2 times 10 minus 3..

I get that the long side is SU and ST and UT

I get it now!!

9 is the short side, 9 times 2 is 18. 18 minus 3 is 15.

Aw, I thought I did it right..

we want to find x
so we concentrate on just the median XT
it can be proved that
2* XY = YT

(2*2 - 1) 10
1x = 10
x= 10

do you see the "length" of XY ?

well XT = 10, and XY is half of XT, so XY=5 ?

yes, that is good thinking.
but according to the label in your picture XY is also what ?

Umm, X is the centroid but I'm not exactly sure what Y is..

XY is way to say, "the line segment joining X to Y"

and that line segment from X to Y has a label in your picture

in other words, they say the length of XY is (2x-3)

using XY=5 (which you figured out up above)
you can write
2x-3 = 5
and now "solve for x"