Rectangle Diagonal Calculator – Pythagorean Theorem
Calculate rectangle diagonal using Pythagorean theorem
Table of Contents
How to Use
- Enter the length of the rectangle
- Enter the width of the rectangle
- Click calculate to find the diagonal
- View the step-by-step formula breakdown
Rectangle Diagonal Formula
The diagonal of a rectangle can be calculated using the Pythagorean theorem. Since the diagonal forms a right triangle with the length and width, we can use: d = √(l² + w²)
Formula: Diagonal = √(Length² + Width²)
The Pythagorean Theorem
The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) equals the sum of the squares of the other two sides: a² + b² = c²
In a rectangle, the diagonal is the hypotenuse, and the length and width are the two legs of the right triangle.
Examples
- Rectangle 3 × 4: Diagonal = √(9 + 16) = √25 = 5
- Rectangle 5 × 12: Diagonal = √(25 + 144) = √169 = 13
- Rectangle 8 × 6: Diagonal = √(64 + 36) = √100 = 10
- Square 5 × 5: Diagonal = √(25 + 25) = √50 ≈ 7.07
Practical Applications
- TV screens: Screen sizes are measured diagonally
- Construction: Checking if corners are square (3-4-5 rule)
- Furniture: Determining if furniture fits through doorways
- Sports: Calculating distances across rectangular fields
- Design: Creating diagonal patterns and layouts
Frequently Asked Questions
- Why are TV screens measured diagonally?
- TV screens are measured diagonally because it provides a single number that represents the overall size regardless of aspect ratio. A 55-inch TV has a diagonal measurement of 55 inches, making it easy to compare different TVs.
- What is the 3-4-5 rule in construction?
- The 3-4-5 rule is a practical application of the Pythagorean theorem used to check if corners are square (90°). If you measure 3 units on one side, 4 units on the other, and the diagonal is exactly 5 units, the corner is perfectly square.
- How do I find the length if I know the diagonal and width?
- Rearrange the formula: Length = √(Diagonal² - Width²). For example, if the diagonal is 10 and width is 6, then length = √(100 - 36) = √64 = 8.
- Does a rectangle have two diagonals?
- Yes, a rectangle has two diagonals that are equal in length. They connect opposite corners and bisect each other (cross at their midpoints). Both diagonals have the same length: √(l² + w²).