1. **State the problem:** We are given the perimeter formula for a rectangle: $$P = 2(x + y)$$ where $x$ and $y$ are the lengths of the sides. 2. **Formula and explanation:** The perimeter $P$ of a rectangle is the total distance around the rectangle, calculated by adding the lengths of all four sides. Since opposite sides are equal, the formula simplifies to $$P = 2(x + y)$$. 3. **Given expressions:** - a = , 2 4 (ambiguous, likely incomplete) - b = , P : 2 (likely means $b = \frac{P}{2}$) - c =; P, 2 (ambiguous) - d = P - 2 4. **Interpreting and simplifying $b = \frac{P}{2}$:** $$b = \frac{P}{2} = \frac{2(x + y)}{2}$$ 5. **Cancel common factors:** $$b = \frac{\cancel{2}(x + y)}{\cancel{2}} = x + y$$ 6. **Explanation:** Dividing the perimeter by 2 gives the sum of the lengths of two adjacent sides, $x + y$. 7. **Final answer:** $$b = x + y$$