1. **Stating the problem:** We have a large rectangle with width 17 and height 14. Inside it, there is a smaller rectangle centered inside with width 9 and height $x$. We need to find the value of $x$ without measuring. 2. **Understanding the problem:** The smaller rectangle is centered inside the larger one. This means the vertical space above and below the smaller rectangle inside the larger one is equal. 3. **Using the given dimensions:** The height of the larger rectangle is 14. The height of the smaller rectangle is $x$. 4. **Finding the vertical margins:** The total vertical space outside the smaller rectangle inside the larger one is $14 - x$. Since the smaller rectangle is centered, the space above and below it is equal, so each margin is \frac{14 - x}{2}. 5. **Using the horizontal dimension for reference:** The width of the larger rectangle is 17. The width of the smaller rectangle is 9. The horizontal margins are \frac{17 - 9}{2} = 4. 6. **Relating the vertical and horizontal margins:** The problem states the figures are reduced in size proportionally. Assuming the vertical margin equals the horizontal margin (since the smaller rectangle is centered and the problem implies proportional reduction), we set: $$\frac{14 - x}{2} = 4$$ 7. **Solving for $x$:** $$14 - x = 8$$ $$x = 14 - 8 = 6$$ **Final answer:** $$x = 6$$