1. What is the Diagonal of Rectangle Formula?

The diagonal of a rectangle can be calculated using the perimeter and area with the formula: \( d = \frac{1}{2} \times \sqrt{P^2 - (8 \times A)} \), where P is the perimeter and A is the area of the rectangle.

2. How Does the Calculator Work?

The calculator uses the diagonal formula:

Where:

• \( d \) — Diagonal of the rectangle (m)
• \( P \) — Perimeter of the rectangle (m)
• \( A \) — Area of the rectangle (m²)

Explanation: This formula is derived from the relationship between the sides of a rectangle, its perimeter, area, and diagonal length.

3. Importance of Diagonal Calculation

Details: Calculating the diagonal of a rectangle is important in various fields including construction, engineering, and design, as it helps determine the longest straight-line distance within the rectangle.

4. Using the Calculator

Tips: Enter the perimeter and area of the rectangle. Both values must be positive numbers. The calculator will compute the diagonal length.

5. Frequently Asked Questions (FAQ)

Q1: What units should I use for input?
A: Use consistent units (e.g., meters for perimeter and square meters for area). The result will be in the same linear unit.

Q2: Can this formula be used for squares?
A: Yes, since a square is a special case of a rectangle, this formula works for squares as well.

Q3: What if the calculated value under the square root is negative?
A: This would indicate invalid input values, as a rectangle with the given perimeter and area cannot exist.

Q4: How accurate is this calculation?
A: The calculation is mathematically exact for the given inputs, assuming they represent a valid rectangle.

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