Explanation:

- We have a right-angled triangle ABC with sides 5 cm, 12 cm, and 13 cm.

- The side measuring 13 cm is the hypotenuse since it is the longest.

- We need to find the length of the perpendicular, p, drawn from vertex A to the hypotenuse BC.

- In a right triangle, the area can also be calculated using the perpendicular height: \((1/2) \times \text{base} \times \text{height}\).

- Area using the two legs: \((1/2) \times 5 \times 12 = 30\).

- Area using hypotenuse (base BC) and p: \((1/2) \times 13 \times p = 30\).

- Solving for p gives: \(13p = 60\).

So, the answer is option 3: 60.