1. **State the problem:** We have a laptop screen with a diagonal length of 15.6 inches and a height of 7.8 inches. We need to find the width of the screen. 2. **Formula used:** The screen forms a right triangle where the diagonal is the hypotenuse, and the height and width are the legs. We use the Pythagorean theorem: $$\text{diagonal}^2 = \text{height}^2 + \text{width}^2$$ 3. **Apply the formula:** Let $w$ be the width. Then: $$15.6^2 = 7.8^2 + w^2$$ 4. **Calculate squares:** $$243.36 = 60.84 + w^2$$ 5. **Isolate $w^2$:** $$w^2 = 243.36 - 60.84$$ $$w^2 = 182.52$$ 6. **Find $w$ by taking the square root:** $$w = \sqrt{182.52}$$ $$w \approx 13.51$$ 7. **Answer:** The width of the screen is approximately **13.51 inches**.