Given that the length of the rectangle is 3 feet longer than the width, and the perimeter is 18 feet, let's determine which choice satisfies these conditions.

Let:

• The width of the rectangle be $w$.
• The length of the rectangle be $w + 3$.

The perimeter of a rectangle is given by the formula: $P = 2(\text{length} + \text{width})$ Substituting the expressions for length and width: $18 = 2((w + 3) + w)$

Now, we simplify the equation: $18 = 2(2w + 3)$ $18 = 4w + 6$ Subtracting 6 from both sides: $12 = 4w$ Dividing both sides by 4: $w = 3$

Thus, the width is 3 feet, and the length is $w + 3 = 6$ feet.

The correct dimensions of the rectangle are:

• Width = 3 feet
• Length = 6 feet.

Would you like me to provide more details or answer any questions?

Relative Questions:

1. How would the dimensions change if the perimeter was increased to 24 feet?
2. What happens to the dimensions if the length is 5 feet longer than the width?
3. How can we apply this method to other shapes with different perimeter formulas?
4. How does the formula for perimeter change if the shape was a square?
5. What would the area of this rectangle be with the given dimensions?

Tip:

Always double-check that your values satisfy all conditions of the problem, like ensuring the perimeter equation holds after solving for dimensions.