Calculate the length of BC given the information about quadrilateral ABCD and triangle ABD.

Here are the calculations for the quadrilateral ABCD:

a) The length of BC

Step 1: Find $\angle ADB$ in $\triangle ABD$.
Given $AB = 17$ cm, $AD = 16$ cm, and $BD = 17$ cm.
Using the Law of Cosines in $\triangle ABD$:

$$AB^2 = AD^2 + BD^2 - 2(AD)(BD) \cos(\angle ADB)$$ $$17^2 = 16^2 + 17^2 - 2(16)(17) \cos(\angle ADB)$$ $$$$