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What is the length of QS?

What is the length of QS?-example-1

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Answer:

Explanation:

What is the length of QS?-example-1
User Ethem
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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

User Leenasn
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