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

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
Transcript text: 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
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Solution

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Solution Steps

Step 1: Understand the problem

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.

Step 2: Recall the formula for the perimeter of a rectangle

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: \[ \text{length} + \text{width} = 9 \]

Step 3: Check each choice against the conditions

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.
Step 4: Identify the correct choice

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

The correct answers are A and C.

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