1. **State the problem:** Determine if the lengths 2.3, 1.5, and 3.4 can form a triangle. 2. **Recall the triangle inequality theorem:** For any triangle with sides $a$, $b$, and $c$, the sum of the lengths of any two sides must be greater than the length of the remaining side. This means: $$a + b > c$$ $$a + c > b$$ $$b + c > a$$ 3. **Apply the theorem to the given lengths:** - Check $2.3 + 1.5 > 3.4$: $$2.3 + 1.5 = 3.8 > 3.4$$ (True) - Check $2.3 + 3.4 > 1.5$: $$2.3 + 3.4 = 5.7 > 1.5$$ (True) - Check $1.5 + 3.4 > 2.3$: $$1.5 + 3.4 = 4.9 > 2.3$$ (True) 4. **Conclusion:** Since all three inequalities hold true, the lengths 2.3, 1.5, and 3.4 can form a triangle.