need answer

Question

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846

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In the diagram below, we have MN is parallel to PQ. We also know that OM=9, OQ=6, and PN=25.

Find OP

https://latex.artofproblemsolving.com/3/d/2/3d2295937acd447e223df6e9b0f7f3cf318d194f.png

Saketh Oct 8, 2019

CoolStuffYT · Answer 1 · 2019-10-08T10:38:35

If triangle OPQ's side lengths are 2/3 of OMN, then PN can be split so that OP is 2/3 of ON.

Basically, OP is 2/3 of ON. Together, they make up 25 (PN).

Can you solve from here?

CPhill · Answer 2 · 2019-10-08T11:47:21

Since MN is parallel to PQ, then triangle MNO is similar to triangle QPO

Then

OM / OQ = ON/ OP

9/6 = ON/ OP

3/2 = ON/OP

Then PN is divided into 5 equal parts and OP is 2 of them

So

OP = (2/5)PN = (2/5) 25 = 10