1. Problem: The length of a rectangular jigsaw puzzle is 12 cm more than its width, and the area is 640 cm². Find the width and length of the jigsaw puzzle. 2. Define the variable: Let $w$ be the width of the jigsaw puzzle in cm. 3. Express length in terms of width: length $= w + 12$. 4. Write the equation for area using width and length: $$w(w + 12) = 640$$ 5. Expand and simplify to get a quadratic equation: $$w^2 + 12w = 640$$ $$w^2 + 12w - 640 = 0$$ 6. Factor the quadratic equation: $$(w + 32)(w - 20) = 0$$ 7. Solve for $w$ using the Null Factor Law: $$w + 32 = 0 \Rightarrow w = -32$$ (not feasible since width cannot be negative) $$w - 20 = 0 \Rightarrow w = 20$$ 8. Find the length: $$length = 20 + 12 = 32$$ 9. Final answer: The dimensions of the jigsaw puzzle are width $20$ cm and length $32$ cm. 10. Check: Area $= 20 \times 32 = 640$ cm², which matches the given area, so the answer is correct.