Question

NO LINKS!! Please help me with this problem Part 1p​

Answer 1

205 m

Explanation:

As line segment NO is parallel to LM and intersects sides KL and MK, the corresponding interior angles of triangles KLM and KNO are congruent.

Angle-Angle similarity states that if any two angles of a triangle are equal to any two angles of another triangle, then the two triangles are similar to each other.

In similar triangles, corresponding sides are always in the same ratio.

Therefore, for similar triangles KLM and KNO:

`\implies \sf KN:KL=KO:KM=NO:LM`

From inspection of the given diagram:

• KL = (180 + 70) m
• KN = 180 m
• NO = 147.6 m

Therefore:

`\implies \sf 180:(180 + 70)=147.6:LM`

`\implies \sf 180:250=147.6:LM`

`\implies \sf (180)/(250)=(147.6)/(LM)`

`\implies \sf 180LM=36900`

`\implies \sf LM=(36900)/(180)`

`\implies \sf LM=205\;m`

Answer 2

• 205 m

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Observations

• LM⊥LK,
• ON⊥LK,
• MLK and ONK are right triangles

Conclusion

• Triangles MLK and ONK are similar.

Corresponding sides of similar triangles are proportional.

Set equation and find the missing length.

• LM/ON = LK/NK

• LM/147.6 = (70 + 180)/180
• LM/147.6 = 250/180
• LM/147.6 = 25/18
• LM = 147.6*25/18
• LM = 205