Questions: Without actually solving the problem, choose the correct solution by deciding which choice satisfies the given conditions. The length of a rectangle is 3 feet longer than the width. The perimeter is 18 feet. Find the dimensions of the rectangle. Which choice satisfies the given conditions? A. length = 5 feet; width = 4 feet B. length = 5 feet; width = 2 feet C. length = 6 feet; width = 3 feet

Solution Steps

The problem states that the length of a rectangle is 3 feet longer than its width, and the perimeter is 18 feet. We are asked to determine which of the given choices satisfies these conditions.

The perimeter $P$ of a rectangle is given by: $$P = 2 \times (\text{length} + \text{width})$$ Given that $P = 18$ feet, we can write: $$2 \times (\text{length} + \text{width}) = 18$$ Simplifying, we get: $$\text{length} + \text{width} = 9$$

We need to check which choice satisfies both:

1. The length is 3 feet longer than the width.
2. The sum of the length and width is 9 feet.

Choice A: length = 5 feet; width = 4 feet

• Check condition 1: $5 = 4 + 3$ → True.
• Check condition 2: $5 + 4 = 9$ → True.

Choice B: length = 5 feet; width = 2 feet

• Check condition 1: $5 = 2 + 3$ → True.
• Check condition 2: $5 + 2 = 7$ → False.

Choice C: length = 6 feet; width = 3 feet

• Check condition 1: $6 = 3 + 3$ → True.
• Check condition 2: $6 + 3 = 9$ → True.

Both Choice A and Choice C satisfy the conditions. However, since the problem asks to choose the correct solution, we can conclude that both A and C are valid solutions.

Final Answer