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