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

[lorddarkhelmet]

Really Desperate For Help!

Homework Statement

Quad MNTS ~ Quad MOPR Find the length of PQ

Homework Equations

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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

 

[Integral]

I do not see a Q in your diagram. Did you mean PO?

 

[HallsofIvy]

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.