Answer: 16 units
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Work Shown:
x = length of PQ
3x-20 = length of QS, since its 20 less than 3 times PQ
The triangles are similar (we can prove this through the AA similarity theorem), so we can set up a proportion like shown below to solve for x.
PT/RS = PQ/QS
6/8 = x/(3x-20)
6(3x-20) = 8x ..... cross multiplying
18x-120 = 8x
18x-8x = 120
10x = 120
x = 120/10
x = 12
So PQ is 12 units long.
This then means QS = 3x-20 = 3*12-20 = 36-20 = 16
