Explanation:

- The given triangle has sides measuring 5 cm, 12 cm, and 13 cm.

- This is a right-angled triangle, with 13 cm being the hypotenuse.

- The area of the triangle can be calculated using the formula: Area = (1/2) * base * height = (1/2) * 5 cm * 12 cm = 30 cm².

- To find the smallest altitude, use the formula: Altitude = (2 * Area) / Base.

- Calculate for each side:

- Altitude to 5 cm side: (2 * 30) / 5 = 12 cm.

- Altitude to 12 cm side: (2 * 30) / 12 = 5 cm.

- Altitude to 13 cm hypotenuse: (2 * 30) / 13 ˜ 4.6 cm.

- The smallest altitude is about 4.6 cm.

The correct answer is option: 4 - 4.6

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