1. **Problem Statement:** Given a triangle ABC with side BC = 3.4 cm, side AB = 7.2 cm, and altitude AD perpendicular to BC measuring 1.9 cm, find the length of segment DE on BC which is 3.4 cm. 2. **Understanding the problem:** We are given a triangle with a perpendicular altitude from vertex A to side BC. The altitude AD is 1.9 cm, and BC is 3.4 cm. We want to analyze the triangle and the segment DE on BC. 3. **Formula and concepts:** - The altitude in a triangle is the perpendicular segment from a vertex to the opposite side. - The area of triangle ABC can be calculated using the base BC and altitude AD: $$\text{Area} = \frac{1}{2} \times BC \times AD$$ - Using the Pythagorean theorem, we can find other sides if needed. 4. **Calculate the area of triangle ABC:** $$\text{Area} = \frac{1}{2} \times 3.4 \times 1.9 = 3.23 \text{ cm}^2$$ 5. **Check side AB:** Given AB = 7.2 cm, which is the length from A to B. 6. **Using Pythagoras theorem in triangle ABD:** Since AD is perpendicular to BC, triangle ABD is right-angled at D. Let BD = x, then: $$AB^2 = AD^2 + BD^2$$ $$7.2^2 = 1.9^2 + x^2$$ $$51.84 = 3.61 + x^2$$ $$x^2 = 51.84 - 3.61 = 48.23$$ $$x = \sqrt{48.23} \approx 6.95 \text{ cm}$$ 7. **Check if BD + DC = BC:** Since BC = 3.4 cm, but BD is approximately 6.95 cm, which is greater than BC, this suggests a discrepancy or that the triangle is not drawn to scale or the given data may have an error. 8. **Conclusion:** Based on the given data, the segment DE on BC is 3.4 cm as stated, but the calculations show inconsistency with the given side AB and altitude AD. **Final answer:** The segment DE on BC is 3.4 cm as given.