we know that
RT=TQ -----> given problem
Applying the Pythagoras Theorem
In the right triangle RTS
[tex]RS^{2}=RT^{2}+TS^{2}[/tex]
In the right triangle TQS
[tex]QS^{2}=TQ^{2}+TS^{2}[/tex]
remember that
RT=TQ
therefore
RS=QS
substitute the values
[tex](3x+2)=(5x-8)[/tex]
solve for x
[tex]5x-3x=2+8[/tex]
[tex]2x=10[/tex]
[tex]x=5\ units[/tex]
Find the value of segment QS
[tex]QS=5x-8=5*5-8=17\ units[/tex]
The answer is
The length of segment QS is [tex]17\ units[/tex]
