To determine the length of BC, we can use the Pythagorean theorem, as the figure contains right triangles.

Steps:

1. Identify the given dimensions:

   • $AD = 10 \, \text{cm}$ (hypotenuse of triangle $ADC$),
   • $DC = 3 \, \text{cm}$ (one leg of triangle $ADC$),
   • $AB = 9 \, \text{cm}$ (height).

2. Recognize that triangle $ADC$ is a right triangle, where $AD$ is the hypotenuse, $DC$ is one leg, and $AC$ is the other leg.

3. Apply the Pythagorean theorem to find $AC$ (the horizontal distance from $A$ to $C$):

   $AD^2 = AC^2 + DC^2$ Substituting the known values: $10^2 = AC^2 + 3^2$ Simplify: $100 = AC^2 + 9$ $AC^2 = 91$ $AC = \sqrt{91} \, \text{cm}$

4. Since $AB$ is vertical and has a height of $9 \, \text{cm}$, the total horizontal length $BC$ is the sum of $AC$ and $DC$. Therefore: [ BC = 9 cm combin divide clarform /i maximum