Question

Triangles and Parallel Lines‼️ Can someone help me please❓ Find OM? OP=9, ON=32, and OQ=12

Answer 1

OM = 24

Explanation:

Given that MN and PQ are parallel and PQ intersects the other 2 sides, then it divides those sides proportionally, that is

`(OP)/(PM )` =
`(OQ)/(QN)`, and substituting values

`(9)/(PM)` =
`(12)/(32-12)`, that is

`(9)/(PM)` =
`(12)/(20)` ( cross- multiply )

12PM = 180 ( divide both sides by 12 )

PM = 15

Thus

OM = OP + PM = 9 + 15 = 24