SOLUTION: Parallelogram PQRS has PQ = 8 cm, QR = 9 cm, and diagonal QS = 10 cm. Mark F on RS, exactly 5 cm from S. Let T be the intersection of PF and QS. Find the lengths TS and TQ.

Algebra ->  Customizable Word Problem Solvers  -> Geometry -> SOLUTION: Parallelogram PQRS has PQ = 8 cm, QR = 9 cm, and diagonal QS = 10 cm. Mark F on RS, exactly 5 cm from S. Let T be the intersection of PF and QS. Find the lengths TS and TQ.      Log On

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Question 1154273: Parallelogram PQRS has PQ = 8 cm, QR = 9 cm, and diagonal QS = 10 cm. Mark F on RS, exactly 5 cm from S. Let T be the intersection of PF and QS. Find the lengths TS and TQ.
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!


ΔFST ∽ ΔPQT

%28PQ%29%2F%28FS%29=%28TQ%29%2F%28TS%29

%288%29%2F%285%29=%28TQ%29%2F%28TS%29

TS+%2B+TQ+=+QS+=+8

TS+%2B+TQ+=+8

TQ+=+8-TS

%288%29%2F%285%29=%288-TS%29%2FTS

Cross-multiply:

8%2ATS=5%288-TS%29

Distribute:

8%2ATS=40-5%2ATS

13%2ATS=40

TS=40%2F13

Substitute in

TQ+=+8-TS

TQ+=+8-40%2F13

Get LCD

TQ+=+104%2F13-40%2F13

TQ=64%2F13

Answer: 
TQ=64%2F13=4%2612%2F13
TS=40%2F13=3%261%2F13

Edwin