1. **State the problem:** We need to find the total perimeter of Florence's bedroom by adding the lengths of all four sides. 2. **Convert mixed fractions to improper fractions:** - Side 1: $89 \frac{1}{4} = 89 + \frac{1}{4} = \frac{356}{4} + \frac{1}{4} = \frac{357}{4}$ inches - Side 2: $65 \frac{7}{16} = 65 + \frac{7}{16} = \frac{1040}{16} + \frac{7}{16} = \frac{1047}{16}$ inches - Side 3: $80 \frac{7}{8} = 80 + \frac{7}{8} = \frac{640}{8} + \frac{7}{8} = \frac{647}{8}$ inches - Side 4: $62 \frac{1}{2} = 62 + \frac{1}{2} = \frac{124}{2} + \frac{1}{2} = \frac{125}{2}$ inches 3. **Find a common denominator to add all fractions:** The denominators are 4, 16, 8, and 2. The least common denominator (LCD) is 16. 4. **Convert all fractions to have denominator 16:** - Side 1: $\frac{357}{4} = \frac{357 \times 4}{4 \times 4} = \frac{1428}{16}$ - Side 2: $\frac{1047}{16}$ (already denominator 16) - Side 3: $\frac{647}{8} = \frac{647 \times 2}{8 \times 2} = \frac{1294}{16}$ - Side 4: $\frac{125}{2} = \frac{125 \times 8}{2 \times 8} = \frac{1000}{16}$ 5. **Add all sides:** $$\frac{1428}{16} + \frac{1047}{16} + \frac{1294}{16} + \frac{1000}{16} = \frac{1428 + 1047 + 1294 + 1000}{16} = \frac{4779}{16}$$ 6. **Convert improper fraction to mixed number:** Divide 4779 by 16: $$4779 \div 16 = 298 \text{ remainder } 11$$ So, $$\frac{4779}{16} = 298 \frac{11}{16}$$ 7. **Final answer:** The total perimeter of the room is $\boxed{298 \frac{11}{16}}$ inches.