Question

Consider the diagram. The length of segment QS__ is units.

Answer 1

The Length of Segment QS is 17 units.

Answer 2

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 $17\ units$