1. **Problem Statement:** We have a diagonal line crossing through 12 congruent squares arranged in two offset rows, forming a stepped shape. We need to find the value of $\cos(x)$, where $x$ is the angle between the diagonal line and the horizontal at the bottom-left corner. 2. **Understanding the figure:** Each square is congruent, so all sides have the same length. Let's denote the side length of each square as $s$. 3. **Analyzing the diagonal line:** The diagonal starts at the bottom-left corner of the first square and ends at the top-right corner of the twelfth square. Since the squares are arranged in two rows offset, the diagonal crosses 12 squares in a stepped manner. 4. **Determining the total horizontal and vertical distances:** - Horizontally, the diagonal moves across 12 squares. Since the squares are arranged in two rows offset, the horizontal distance covered is $12s$. - Vertically, the diagonal rises by the height of 5 squares (since the diagonal crosses 5 squares vertically in the stepped shape). So the vertical distance is $5s$. 5. **Using the definition of cosine:** $$\cos(x) = \frac{\text{adjacent side}}{\text{hypotenuse}} = \frac{\text{horizontal distance}}{\text{length of diagonal}}$$ 6. **Calculating the length of the diagonal:** Using the Pythagorean theorem: $$\text{diagonal} = \sqrt{(12s)^2 + (5s)^2} = s\sqrt{144 + 25} = s\sqrt{169} = 13s$$ 7. **Calculating $\cos(x)$:** $$\cos(x) = \frac{12s}{13s} = \frac{12}{13}$$ 8. **Final answer:** $$\boxed{\frac{12}{13}}$$ This corresponds to option C) 12/13.