1. **State the problem:** We have a rectangle and a square with the same perimeter. The rectangle has width $x+7$ cm and height 7 cm. The square has side length $x+5$ cm. We need to find the value of $x$. 2. **Formula for perimeter:** - Perimeter of rectangle = $2(\text{width} + \text{height})$ - Perimeter of square = $4 \times \text{side}$ 3. **Set up the equation:** Since the perimeters are equal, $$2((x+7) + 7) = 4(x+5)$$ 4. **Simplify inside parentheses:** $$2(x + 14) = 4(x + 5)$$ 5. **Distribute:** $$2x + 28 = 4x + 20$$ 6. **Rearrange terms to isolate $x$:** $$28 - 20 = 4x - 2x$$ $$8 = 2x$$ 7. **Solve for $x$:** $$x = \frac{8}{2} = 4$$ **Final answer:** $x = 4$