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Help would be appreciated a lot!!

In ALMN, LM || OP. Given that NL = 33, NM=44, and NP = 24, find NO.
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Help would be appreciated a lot!! In ALMN, LM || OP. Given that NL = 33, NM=44, and-example-1

1 Answer

4 votes

Answer:

NO= 18

Explanation:

If we dissect the image, we can see that triangle LMN there are two similar triangles; triangle LMN and smaller triangle OPN. By definition of similar triangles, corresponding parts of similar triangles will have the same ratios. So, as we can see, sides NP and NM are corresponding. The ratio of the two sides is 24/44 (just put the smaller side over the longer side). Simplified, the ratio is 6/11. So, we know that the opposite sides' ratio will also be 6/11. So, all we have to do is multiply NL (33) by 6/11, which equals 18.

Check:

24/44=6/11, and 18/33=6/11, so the ratios are the same.

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