1. **Stating the problem:** We have a triangle with a vertical side of length 6 cm and a horizontal base of length 12 cm, which is divided into two smaller segments of 7.5 cm and 2.5 cm. We want to analyze or solve for properties related to this triangle. 2. **Understanding the triangle:** The base is split into two parts: 7.5 cm and 2.5 cm, which sum to 10 cm, but the total base is given as 12 cm. This suggests there might be a missing segment or a misunderstanding. Assuming the base is 12 cm total, and the two segments 7.5 cm and 2.5 cm are part of it, the remaining segment is $12 - (7.5 + 2.5) = 2$ cm. 3. **Using the Pythagorean theorem:** If the triangle is right-angled with the vertical side as height and the base as the horizontal side, the hypotenuse can be calculated. For example, if the vertical side is 6 cm and the base is 12 cm, the hypotenuse $c$ is: $$c = \sqrt{6^2 + 12^2} = \sqrt{36 + 144} = \sqrt{180} = 6\sqrt{5} \approx 13.42 \text{ cm}$$ 4. **If the problem involves the segments 7.5 cm and 2.5 cm:** These could represent parts of the base divided by a point, possibly for similar triangles or other properties. Without further information, we can note the segments and their sum. 5. **Summary:** The triangle has a vertical side of 6 cm, a base of 12 cm, and segments on the base of 7.5 cm and 2.5 cm. The hypotenuse is approximately 13.42 cm if the triangle is right-angled. Final answer: The hypotenuse length is approximately $13.42$ cm if the triangle is right-angled with the given sides.