1. **State the problem:** We need to find the hypotenuse of a right triangle with legs measuring 2.17 and 3.25. 2. **Formula used:** The Pythagorean theorem states that for a right triangle with legs $a$ and $b$, and hypotenuse $c$, the relationship is: $$c = \sqrt{a^2 + b^2}$$ 3. **Apply the formula:** Substitute $a = 2.17$ and $b = 3.25$: $$c = \sqrt{(2.17)^2 + (3.25)^2}$$ 4. **Calculate squares:** $$(2.17)^2 = 4.7089$$ $$(3.25)^2 = 10.5625$$ 5. **Sum the squares:** $$4.7089 + 10.5625 = 15.2714$$ 6. **Find the square root:** $$c = \sqrt{15.2714} \approx 3.91$$ 7. **Conclusion:** The hypotenuse of the triangle is approximately $3.91$ units.