1. What is the Length and Width Calculation?

This calculator determines the possible length and width dimensions of a rectangle when you know the total square footage and perimeter. It solves the quadratic equation derived from the area and perimeter formulas.

2. How Does the Calculator Work?

The calculator uses the mathematical formula:

Where:

• \( L \) — Length (feet)
• \( P \) — Perimeter (feet)
• \( SF \) — Square Feet (ft²)

Explanation: This formula is derived from solving the system of equations: Area = Length × Width and Perimeter = 2 × (Length + Width).

3. Importance of Dimension Calculation

Details: Calculating length and width from known area and perimeter is essential for construction planning, landscaping, room layout design, and various engineering applications where rectangular dimensions need to be determined.

4. Using the Calculator

Tips: Enter the total square footage and perimeter in the respective fields. Both values must be positive numbers. The calculator will provide two possible dimension combinations that satisfy both area and perimeter constraints.

5. Frequently Asked Questions (FAQ)

Q1: Why are there two possible solutions?
A: Because length and width are interchangeable in a rectangle, the equation yields two mathematically valid solutions that represent the same physical dimensions.

Q2: What if I get an error message?
A: The error occurs when the perimeter squared is less than 16 times the area, which is mathematically impossible for a rectangle. Check your input values.

Q3: Can this be used for squares?
A: Yes, for a square, both solutions will be identical since length equals width.

Q4: What units should I use?
A: Use consistent units (feet for both perimeter and dimensions, square feet for area) for accurate results.

Q5: Are there limitations to this calculation?
A: This only works for rectangles. For other shapes, different formulas are required to determine dimensions from area and perimeter.