Finding the Length of PQ in Quadrilateral MNTS and MOPR Using Ratios

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The discussion revolves around finding the length of segment PQ in the similar quadrilaterals MNTS and MOPR. The user has calculated a ratio of 5/4 but is confused about the dimensions and corresponding segments. The lengths from O to N and N to M are given as 16 and 24, respectively, leading to a total length of OM as 40, which contradicts the 5/4 ratio. Clarification is sought on whether PQ refers to PO, as PO corresponds to TN in the other quadrilateral, which has a length of 12. The conclusion suggests that PO should be calculated using the correct ratio based on the established lengths.
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Homework Statement



Quad MNTS ~ Quad MOPR Find the length of PQ

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The Attempt at a Solution



i have done numerous attempts and i can't figure out what to do after i get the ratio of 5/4
 

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I do not see a Q in your diagram. Did you mean PO?
 
If I am reading your picture correctly, the distance from O to N is 16 and the distance from N to M is 24. That means that the length of OM is 16+ 24= 40. The ratio of any side of the larger quad to the corresponding side of the smaller is 40/24 which is NOT 5/4!

Assuming you do mean PO, PO in quadrilateral MOPR corresponds to TN in quadrilateral MNTS which, according to your diagram has a length of 12. PO must be that length times the ratio.
 

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