Question 91774
This problem can be solved by using Pythagorean-theorem twice.

First find QS:  {{{QS^2 = QP^2 - PS^2}}}

{{{QS^2 = 13^2 - 12^2 }}}

{{{QS^2}}} = 25

QS = 5

Then RS = QR - QS = 13 - 5 = 8

PR = {{{sqrt(PS^2 + RS^2)}}}

PR = {{{sqrt(144 + 64)}}}

PR = {{{sqrt(208)}}}

PR = {{{4*sqrt(13)}}}

or PR = 14.42