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`