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:

`(AC)/(BC) = (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:

`(AC)/(BC) = (BC)/(CD)`

`(18)/(m) = (m)/(7)`
Solving for
`m`:

`m^2=(18)(7)`

`m^2=126`

`m= √(126)`

We can conclude that the correct answer is: D
`√(126)`