Find the length of BC, in simplest radical form.

9514 1404 393

  BC = 16 +12√3

Step-by-step explanation:

In the attached, we see that ∆ABE is a 30°-60°-90° triangle with AB the short side and BE the hypotenuse. Then BE = 2·AB = 12√3.

EC is the side opposite AD in parallelogram ADCE, so is the same length, 16.

The length BC is ...

  BC = EC +BE

 BC = 16 +12√3