1. What is the Length of Rectangle Formula?

The formula calculates the length of a rectangle when given its perimeter and area. It is derived from the relationships between length, width, perimeter, and area of a rectangle.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( l \) — Length of the rectangle (m)
• \( P \) — Perimeter of the rectangle (m)
• \( A \) — Area of the rectangle (m²)

Explanation: The formula is derived from solving the system of equations P = 2(l + w) and A = l × w for the length l.

3. Importance of Rectangle Dimensions

Details: Calculating accurate rectangle dimensions is crucial for various applications including construction, manufacturing, landscaping, and geometric problem solving where perimeter and area are known but individual dimensions need to be determined.

4. Using the Calculator

Tips: Enter the perimeter and area values in meters and square meters respectively. Both values must be positive numbers. The calculator will validate if the inputs can form a real rectangle.

5. Frequently Asked Questions (FAQ)

Q1: What if the calculator shows an error?
A: This means the given perimeter and area cannot form a real rectangle. For a given perimeter, the maximum possible area is when the rectangle is a square.

Q2: Can this formula be used for squares?
A: Yes, when the rectangle is a square, the formula will correctly calculate the side length.

Q3: What units should I use?
A: Use consistent units (meters for perimeter, square meters for area). The calculator will return length in the same unit as the perimeter input.

Q4: How accurate is the calculation?
A: The calculation is mathematically exact, but results are rounded to 4 decimal places for practical use.

Q5: Can I use this for other quadrilaterals?
A: No, this formula is specific to rectangles where opposite sides are equal and all angles are 90 degrees.