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Find n in the picture provided please!

Find n in the picture provided please!-example-1

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Answer:

n = 16

Explanation:

LO is parallel to MN since they both make a right angle with KM.

Therefore, triangles KLO and KMN are similar triangles.

As corresponding sides of similar triangles are always in the same ratio:

KL : KM = LO : MN

From inspection of the given diagram:

  • KL = 30
  • KM = 30 + 15 = 45
  • LO = n
  • MN = 24

Substitute the values into the ratio and solve for n:


\implies \sf KL : KM = LO : MN


\implies \sf 30: 45= n: 24


\implies \sf (30)/(45)=(n)/(24)


\implies \sf n=24 \cdot (30)/(45)


\implies \sf n=(720)/(45)


\implies \sf n=16

Therefore, the value of n is 16.

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