Amber O.

asked • 04/17/19

college geometry

In the diagram below, ST⎯⎯⎯⎯⎯∥PQ⎯⎯⎯⎯⎯⎯∥LM⎯⎯⎯⎯⎯⎯∥CD⎯⎯⎯⎯⎯⎯.  Furthermore, SP=4x−1,  QM=x−3,  TQ=x+5,  , and PL=x+6.  Find the ratio of LC to MD.

(Note that the diagram may not be drawn to scale.)

Exam Image

a) 73

b) 52

c) 37

d) More information is needed to solve this problem.

e) 25

f) None of the above



2 Answers By Expert Tutors

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Greg F. answered • 04/17/19

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Amber O.

I solved the proportion and got 9 and -1. I'm not sure what to do from here.
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04/17/19

Greg F.

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Hi Amber, I'm glad you gave it a shot! You're really close! So 9 and -1 are the two values for x. Only 9 is a valid answer because if x = -1, then that would give us negative values for the lengths of the lines in the diagram, which is not possible in this context. So now all you have to do is take 9 and plug it in for x into either ratio (4x-1)/(x+5) or (x+6)/(x-3). Since both ratios are equal to LC/MD, either ratio will give you the same answer. PS you will have to simplify the ratio after you plug in for x to get one of the multiple choice answers.
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04/17/19

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