To solve for the length of the rectangle, we can use the formula for the perimeter of a rectangle:

$\text{Perimeter} = 2 \times (\text{length} + \text{width})$

Given:

• Perimeter = 204 feet
• Width = 45 feet

Step 1: Substitute the known values into the formula

$204 = 2 \times (\text{length} + 45)$

Step 2: Divide both sides by 2 to simplify

$102 = \text{length} + 45$

Step 3: Solve for the length by subtracting 45 from both sides

$\text{length} = 102 - 45 = 57$

Answer

The length of the rectangle is 57 feet.

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Related Questions

1. If the width were increased to 50 feet, what would the new perimeter be?
2. What would be the area of the rectangle with the original dimensions?
3. If the perimeter was doubled, what would be the new length?
4. What is the ratio of the length to the width in this rectangle?
5. If the length was reduced by 5 feet, what would be the new perimeter?

Tip:

For rectangles, knowing either the perimeter or area can often lead to finding unknown side lengths by setting up and solving equations.