For the length of BC. From the diagram, ABC is a right-angled triangle with the right angle at B.

The problem asks for the length of BC. From the diagram, $\triangle ABC$ is a right-angled triangle with the right angle at B.
The given lengths are $AB = 7$ cm.
The diagram indicates $AC = 20$ cm. (Note: The text states $AD = 12$ cm, but this length is not directly used for finding BC in $\triangle ABC$. We will use $AC = 20$ cm as shown in the diagram for $\triangle ABC$.)

For a right-angled triangle, the Pythagorean theorem states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In $\triangle ABC$:

Substitute $AB = 7$ cm and $AC = 20$ cm:

Subtract 49 from both sides:

Take the square root of both sides:

Calculating the numerical value and rounding to two decimal places:

The length of BC is $\text{18.73 cm}$.