1. **Problem 17:** The area of the rectangle exceeds the area of the square by 2 cm². Find $x$. 2. **Step 1: Define the areas.** - Rectangle dimensions: height = $x - 1$, width = $x + 2$ - Square side length = $x$ 3. **Step 2: Write the area expressions.** - Area of rectangle = $(x - 1)(x + 2)$ - Area of square = $x^2$ 4. **Step 3: Set up the equation from the problem statement.** $$\text{Area of rectangle} = \text{Area of square} + 2$$ $$ (x - 1)(x + 2) = x^2 + 2 $$ 5. **Step 4: Expand and simplify.** $$ x^2 + 2x - x - 2 = x^2 + 2 $$ $$ x^2 + x - 2 = x^2 + 2 $$ 6. **Step 5: Subtract $x^2$ from both sides.** $$ x - 2 = 2 $$ 7. **Step 6: Solve for $x$.** $$ x = 2 + 2 = 4 $$ 8. **Step 7: Verify the solution.** - Rectangle area: $(4 - 1)(4 + 2) = 3 \times 6 = 18$ - Square area: $4^2 = 16$ - Difference: $18 - 16 = 2$ which matches the problem statement. **Final answer:** $x = 4$