1. The problem asks for the expression representing the perimeter of a rectangle with width $(10f + 8)$ cm and length $(5f - 3)$ cm. 2. Recall the formula for the perimeter $P$ of a rectangle: $$P = 2(\text{length} + \text{width})$$ 3. Substitute the given expressions for length and width: $$P = 2((5f - 3) + (10f + 8))$$ 4. Combine like terms inside the parentheses: $$P = 2(5f - 3 + 10f + 8) = 2(15f + 5)$$ 5. Distribute the 2: $$P = 2 \times 15f + 2 \times 5 = 30f + 10$$ 6. Therefore, the expression for the perimeter is $30f + 10$ centimeters. The correct answer is: 30 f + 10