Question 461150
Let W be the point on SR such that |SW| = |PT|.  Let x = |SW|.  By the given, |SR| = |ST| = 10.  Then {{{(ST)^2 = (SW)^2 + 6^2}}}, or {{{10^2 = x^2 + 6^2}}}, or 

{{{100 = x^2 + 36}}}, or x = 8 after a little algebra.

Then {{{(RT)^2 = 6^2 + (10 - x)^2}}}, or {{{(RT)^2 = 6^2 + 2^2 = 40}}}, or

{{{abs(RT) = sqrt(40) = 2sqrt(10)}}} cm.