1. **Problem statement:** We have a large rectangle ABCD composed of two smaller rectangles joined horizontally. The length AB (and CD) is $x$ cm. The width BC (and AD) is divided into two parts: one smaller rectangle with width 2 cm and the other with width 3 cm. The smaller rectangle on the right is shaded. 2. **Find expressions for the areas:** - The area of the large rectangle ABCD is length times width: $$\text{Area}_{ABCD} = x \times (2 + 3)$$ - The two smaller rectangles have areas: - Right rectangle: $$x \times 2$$ - Left rectangle: $$x \times 3$$ 3. **Write the expressions explicitly:** - $$\text{Area}_{ABCD} = x(2 + 3)$$ - $$\text{Area}_{right} = 2x$$ - $$\text{Area}_{left} = 3x$$ 4. **Show equivalence:** - Simplify the large rectangle area: $$x(2 + 3) = x \times 5 = 5x$$ - Sum of smaller rectangles: $$2x + 3x = 5x$$ 5. **Conclusion:** The area of the large rectangle equals the sum of the areas of the two smaller rectangles, confirming the expressions are equivalent. **Final answer:** $$\text{Area}_{ABCD} = 5x = 2x + 3x$$