Question

Find n in the picture provided please!

Answer 1

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.