1. What is the Quadratic Equation for Length and Width?

This calculator uses the quadratic equation derived from the relationship between area, perimeter, length, and width of a rectangle. Given the perimeter (P) and area (SF), it calculates possible length (L) and width (W) combinations.

2. How Does the Calculator Work?

The calculator uses the quadratic equation:

Where:

• \( L \) — Length (feet)
• \( P \) — Perimeter (feet)
• \( SF \) — Square Footage (square feet)

Explanation: The equation is derived from the system of equations: P = 2(L + W) and SF = L × W. Solving for L gives the quadratic equation shown above.

3. Importance of Length and Width Calculation

Details: Calculating length and width from area and perimeter is essential in various fields including construction, landscaping, interior design, and geometry problems. It helps determine the exact dimensions of rectangular spaces.

4. Using the Calculator

Tips: Enter square footage in ft² and perimeter in feet. Both values must be positive numbers. The calculator will provide both possible solutions (length and width are interchangeable in a rectangle).

5. Frequently Asked Questions (FAQ)

Q1: Why are there two solutions?
A: Because length and width are interchangeable in a rectangle, the equation provides two valid combinations that satisfy both the area and perimeter constraints.

Q2: What if I get "No real solution exists"?
A: This means the discriminant (P² - 16×SF) is negative, indicating that no real rectangle exists with the given area and perimeter values.

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

Q4: What units should I use?
A: Use consistent units (feet for perimeter, square feet for area). The calculator assumes both measurements are in the same unit system.

Q5: How accurate are the results?
A: Results are mathematically exact based on the input values. The calculator rounds to 2 decimal places for practical use.