1. **State the problem:** We have a rectangle with the top side labeled $11x + 2$ and the bottom side labeled $4x + 16$. We need to find the value of $x$. 2. **Recall the property of rectangles:** Opposite sides of a rectangle are equal in length. 3. **Set up the equation:** Since the top and bottom sides are opposite sides, they must be equal: $$11x + 2 = 4x + 16$$ 4. **Solve for $x$:** Subtract $4x$ from both sides: $$11x + 2 - \cancel{4x} = \cancel{4x} + 16 - 4x \Rightarrow 7x + 2 = 16$$ Subtract 2 from both sides: $$7x + 2 - 2 = 16 - 2 \Rightarrow 7x = 14$$ Divide both sides by 7: $$\frac{7x}{\cancel{7}} = \frac{14}{\cancel{7}} \Rightarrow x = 2$$ 5. **Final answer:** $$x = 2$$