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breannao breannao
  • 15-01-2020
  • Mathematics
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Triangles and Parallel Lines‼️ Can someone help me please❓ Find OM? OP=9, ON=32, and OQ=12

Triangles and Parallel Lines Can someone help me please Find OM OP9 ON32 and OQ12 class=

Respuesta :

jimrgrant1 jimrgrant1
  • 15-01-2020

Answer:

OM = 24

Step-by-step explanation:

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

[tex]\frac{OP}{PM }[/tex] = [tex]\frac{OQ}{QN}[/tex], and substituting values

[tex]\frac{9}{PM}[/tex] = [tex]\frac{12}{32-12}[/tex], that is

[tex]\frac{9}{PM}[/tex] = [tex]\frac{12}{20}[/tex] ( cross- multiply )

12PM = 180 ( divide both sides by 12 )

PM = 15

Thus

OM = OP + PM = 9 + 15 = 24

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