1. **Problem statement:** We need to find the value of $x$ in a right triangle where one leg is 2 units, the other leg is $x$ units, and the hypotenuse is 7 units. 2. **Formula used:** The Pythagorean theorem states that for a right triangle with legs $a$ and $b$, and hypotenuse $c$, the relationship is: $$a^2 + b^2 = c^2$$ 3. **Apply the formula:** Here, $a = 2$, $b = x$, and $c = 7$. Substitute these values: $$2^2 + x^2 = 7^2$$ 4. **Simplify:** $$4 + x^2 = 49$$ 5. **Isolate $x^2$:** $$x^2 = 49 - 4$$ $$x^2 = 45$$ 6. **Solve for $x$:** $$x = \sqrt{45}$$ 7. **Simplify the square root if desired:** $$\sqrt{45} = \sqrt{9 \times 5} = 3\sqrt{5}$$ **Answer:** $x = \sqrt{45}$, which corresponds to option C. This means the length of the unknown leg is $\sqrt{45}$ units. The Pythagorean theorem helps us find missing side lengths in right triangles, which is useful in many real-world applications like construction, navigation, and geometry.