1. **Stating the problem:** We have a right triangle divided into two right-angled triangles by a height $a=2$ perpendicular to the base $h$. One segment of the base is $s_1=1$, and we want to find the other measures: $s_2$, $l_1$, and $l_2$. 2. **Known values:** - Height $a=2$ - Segment $s_1=1$ 3. **Using the Pythagorean theorem:** Each smaller right triangle satisfies: $$l_1^2 = a^2 + s_1^2$$ $$l_2^2 = a^2 + s_2^2$$ 4. **Relation between segments:** The total base $h = s_1 + s_2$. 5. **Using the geometric mean property of the altitude in a right triangle:** The altitude $a$ satisfies: $$a^2 = s_1 \times s_2$$ 6. **Calculate $s_2$:** $$2^2 = 1 \times s_2$$ $$4 = s_2$$ 7. **Calculate $l_1$:** $$l_1^2 = 2^2 + 1^2 = 4 + 1 = 5$$ $$l_1 = \sqrt{5}$$ 8. **Calculate $l_2$:** $$l_2^2 = 2^2 + 4^2 = 4 + 16 = 20$$ $$l_2 = \sqrt{20} = \sqrt{4 \times 5} = 2\sqrt{5}$$ 9. **Summary of results:** - $s_2 = 4$ - $l_1 = \sqrt{5}$ - $l_2 = 2\sqrt{5}$ All answers are in simplest radical form.