3. A wall in Miss Wong's dining room is 7 feet long and 9 feet wide. Miss Wong hangs a rectangular mirror with an area of 12 square feet. a. What is the area of the wall not covered by the mirror? b. What could be the length and width of the mirror? How do you know?

Step 1. Find the area of the wall. • The wall is 7 feet by 9 feet, so its area is 7 × 9 = 63 square feet. Step 2. Compute the area not covered by the mirror. • Since the mirror has an area of 12 square feet, the uncovered area is 63 – 12 = 51 square feet. Step 3. Determine possible dimensions of the mirror. • Let the mirror’s length be L and its width be W. We know that L × W = 12 square feet. • There are infinitely many pairs (L, W) of positive numbers that satisfy this equation. Some common factor pairs are:   – 1 foot × 12 feet   – 2 feet × 6 feet   – 3 feet × 4 feet   – 4 feet × 3 feet (which is the same as 3 feet × 4 feet)   – 6 feet × 2 feet   – 12 feet × 1 foot Step 4. Consider practical dimension choices. • Since the mirror is hung on a wall that is 7 feet by 9 feet, the mirror dimensions must be such that the mirror can reasonably fit within these dimensions. • For example, a 3‑foot by 4‑foot mirror (or a 4‑foot by 3‑foot mirror) is a practical choice because both 3 and 4 are less than the wall’s 7‑foot and 9‑foot dimensions. • Other pairs, like 1 foot by 12 feet, might not be as practical (the 12‑foot length would exceed the 9‑foot dimension of the wall). Final Answers: a. The area of the wall not covered by the mirror is 51 square feet. b. One possible set of dimensions for the mirror is 3 feet by 4 feet (since 3 × 4 = 12). In general, any positive numbers L and W satisfying L × W = 12 work, but practical choices must also fit on the 7‑by‑9‐foot wall.