1. What is the Rectangle Dimensions Calculator?

This calculator finds the length and width of a rectangle when you know its perimeter and area. It solves the system of equations formed by the perimeter and area formulas of a rectangle.

2. How Does the Calculator Work?

The calculator uses these formulas:

Where:

• \( P \) — Perimeter of the rectangle
• \( A \) — Area of the rectangle
• \( l \) — Length of the rectangle
• \( w \) — Width of the rectangle

Explanation: The formulas are derived from solving the system of equations P = 2(l + w) and A = l × w simultaneously.

3. Importance of Rectangle Dimensions

Details: Knowing both dimensions of a rectangle is essential in construction, design, and various engineering applications where specific proportions are required.

4. Using the Calculator

Tips: Enter the perimeter and area values. Both must be positive numbers, and the area must satisfy A ≤ (P/4)² (the maximum area for a given perimeter).

5. Frequently Asked Questions (FAQ)

Q1: What if I get an error message?
A: This means no real rectangle exists with the given perimeter and area. The maximum area for a given perimeter P is (P/4)² (a square).

Q2: Can I use this for other quadrilaterals?
A: No, these formulas are specific to rectangles where all angles are 90° and opposite sides are equal.

Q3: What units should I use?
A: Use consistent units for perimeter (linear) and area (square). The results will be in the same linear units.

Q4: Why are there two solutions?
A: The solutions represent length and width, which are interchangeable for a rectangle (a 5×3 rectangle is the same as a 3×5 rectangle).

Q5: What if I only know one dimension?
A: If you know one dimension and either area or perimeter, you can calculate the other dimension directly without needing this calculator.