1. **State the problem:** Find the value of $x$ in each of the given figures. 2. **Figure (1):** The triangle has sides 5, 3, and $x$, with a base length 11. Since the base is 11 and the other two sides are 5 and 3, this suggests a right triangle with the hypotenuse 11. Use the Pythagorean theorem: $$a^2 + b^2 = c^2$$ where $c$ is the hypotenuse. Here, $a = 5$, $b = 3$, and $c = 11$. 3. Calculate $a^2 + b^2$: $$5^2 + 3^2 = 25 + 9 = 34$$ 4. Compare with $c^2$: $$11^2 = 121$$ Since $34 \neq 121$, 11 is not the hypotenuse of this triangle with sides 5 and 3. The problem likely means $x$ is the missing side opposite the right angle, so use the Pythagorean theorem: $$5^2 + 3^2 = x^2$$ $$25 + 9 = x^2$$ $$x^2 = 34$$ $$x = \sqrt{34} \approx 5.83$$ 5. **Figure (2):** The triangle has sides $x$, 6, and 10, with a base length 12. Assuming the right angle is between sides $x$ and 6, and 10 is the hypotenuse. Use the Pythagorean theorem: $$x^2 + 6^2 = 10^2$$ $$x^2 + 36 = 100$$ $$x^2 = 100 - 36 = 64$$ $$x = \sqrt{64} = 8$$ **Final answers:** - Figure (1): $x = \sqrt{34} \approx 5.83$ - Figure (2): $x = 8$