Since triangles ABC and BCD are similar, we can establish a proportion between the lengths of corresponding sides: [tex] \frac{AC}{BC} = \frac{BC}{CD} [/tex]
We can infer from our picture that [tex]BC=m[/tex]. Also we can find the length of AC by adding AD and CD: [tex]AC=AD+CD[/tex] [tex]AC=11+7[/tex] [tex]AC=18[/tex]
Lets replace the values in our proportion: [tex] \frac{AC}{BC} = \frac{BC}{CD} [/tex] [tex] \frac{18}{m} = \frac{m}{7} [/tex] Solving for [tex]m[/tex]: [tex]m^2=(18)(7)[/tex] [tex]m^2=126[/tex] [tex]m= \sqrt{126} [/tex]
We can conclude that the correct answer is: D [tex] \sqrt{126} [/tex]
