1. **State the problem:** Amber wants to tile a bathroom wall measuring 1.2 meters by 2.16 meters using square tiles of side lengths 10 cm, 12 cm, or 18 cm. We need to determine which tile sizes will fit the wall exactly without cutting. 2. **Convert all measurements to the same unit:** - Wall dimensions: 1.2 m = 120 cm, 2.16 m = 216 cm - Tile side lengths: 10 cm, 12 cm, 18 cm 3. **Check if the tiles fit exactly along each dimension:** - For a tile to fit exactly, the wall length must be divisible by the tile side length. 4. **Check 10 cm tiles:** - Along 120 cm: $\frac{120}{10} = 12$ (an integer) - Along 216 cm: $\frac{216}{10} = 21.6$ (not an integer) - So, 10 cm tiles do not fit exactly. 5. **Check 12 cm tiles:** - Along 120 cm: $\frac{120}{12} = 10$ (an integer) - Along 216 cm: $\frac{216}{12} = 18$ (an integer) - So, 12 cm tiles fit exactly. 6. **Check 18 cm tiles:** - Along 120 cm: $\frac{120}{18} = 6.666\ldots$ (not an integer) - Along 216 cm: $\frac{216}{18} = 12$ (an integer) - So, 18 cm tiles do not fit exactly. **Final answer:** Only the 12 cm square tiles will fit the bathroom wall exactly without cutting.