Question

PLEASE PLEASE HELP WITH THIS

Answer 1

Since triangles ABC and BCD are similar, we can establish a proportion between the lengths of corresponding sides:
$\frac{AC}{BC} = \frac{BC}{CD}$

We can infer from our picture that $BC=m$. Also we can find the length of AC by adding AD and CD:
$AC=AD+CD$
$AC=11+7$
$AC=18$

Lets replace the values in our proportion:
$\frac{AC}{BC} = \frac{BC}{CD}$
$\frac{18}{m} = \frac{m}{7}$
Solving for $m$:
$m^2=(18)(7)$
$m^2=126$
$m= \sqrt{126}$

We can conclude that the correct answer is: D $\sqrt{126}$