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:

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

$70+10x = 15x\\\\70 = 15x-10x\\\\5x = 70\\\\x = \frac{70}{5}\\\\x = 14\\\\\text{NM} = 14$

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