Because we know the lines are parallel we can deduce that the triangles are also similar because their angles are congruent. If you don't know which triangles I'm talking about, they are are triangle PTQ and triangle RTS. Knowing that similar triangles have lengths that are in proportion we can say:
[tex] \frac{PT}{QT} = \frac{RT}{ST} [/tex]
Now all we have to do is substitute the values given
[/tex] \frac{18}{21} = \frac{24}{x} [/tex]
We know RT is 24 because RT = PT + RP. We can also simplify 18/21 as 6/7 for simplicity.
6/7 = 24/x
Now we can cross multiply
6x = 168
Divide both sides by 6
x=28
HOWEVER, x only represents ST so we must subtract 21 from 28 to get SQ.
SQ = 28- 21 = 7
Final answer: A) SQ = 7
