Question

In the diagram below, NO is parallel to K L. If KN = 7, NO = 10, and

KL = 15, find the length of N M. Figures are not necessarily drawn to scale. State
your answer in simplest radical form, if necessary.

Answer 1

Answer: 14

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Work Shown:

`\frac{\text{KM}}{\text{NM}} = \frac{\text{KL}}{\text{NO}}\\\\\frac{\text{KN}+\text{NM}}{\text{NM}} = \frac{\text{KL}}{\text{NO}}\\\\(7+x)/(x) = (15)/(10)\\\\10(7+x) = 15x\\\\`

`70+10x = 15x\\\\70 = 15x-10x\\\\5x = 70\\\\x = (70)/(5)\\\\x = 14\\\\\text{NM} = 14`

Side note: The triangles are similar, which allows us to set up the proportion in step 1.