1. **State the problem:** We have three right triangles arranged horizontally. The first triangle has legs 8 (vertical) and 6 (horizontal). The second triangle shares a vertical leg of length 18. The last horizontal segment is labeled $x$. We need to solve for $x$. 2. **Understand the setup:** The triangles are arranged in a zig-zag pattern, so the vertical legs add up and the horizontal legs add up accordingly. 3. **Use the Pythagorean theorem:** For each right triangle, the hypotenuse squared equals the sum of the squares of the legs. 4. **Calculate the hypotenuse of the first triangle:** $$c_1 = \sqrt{8^2 + 6^2} = \sqrt{64 + 36} = \sqrt{100} = 10$$ 5. **Calculate the hypotenuse of the second triangle:** The vertical leg is 18, and the horizontal leg is unknown but related to $x$ and the first horizontal leg. 6. **Assuming the total horizontal length is the sum of the horizontal legs:** The total horizontal length is $6 + x$. 7. **Calculate the hypotenuse of the second triangle:** $$c_2 = \sqrt{18^2 + (x)^2} = \sqrt{324 + x^2}$$ 8. **Since the triangles are arranged in a zig-zag, the hypotenuses are equal:** $$10 = \sqrt{324 + x^2}$$ 9. **Square both sides:** $$10^2 = 324 + x^2$$ $$100 = 324 + x^2$$ 10. **Isolate $x^2$:** $$x^2 = 100 - 324 = -224$$ 11. **Since $x^2$ is negative, this is impossible for a real number $x$. Check the problem setup or assumptions.** 12. **Alternative interpretation:** The middle triangle's vertical leg is 18, and the last horizontal segment is $x$. The total horizontal length is $6 + x$, and the total vertical length is $8 + 18 = 26$. 13. **Calculate the hypotenuse of the large triangle formed by the total vertical and horizontal legs:** $$c = \sqrt{26^2 + (6 + x)^2}$$ 14. **If the hypotenuse equals the sum of the hypotenuses of the smaller triangles, or if the triangles are similar, more information is needed.** 15. **Without additional information, we cannot solve for $x$.** **Final answer:** Cannot solve for $x$ with the given information.