Diagonal of a Rectangle
Length of the diagonal of a rectangle.
Formula
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Example
A 3 × 4 rectangle has diagonal d = √(9+16) = 5.
How it works
A rectangle’s diagonal connects two opposite corners, and that segment forms a right triangle with the rectangle’s length and width. Because the sides meet at 90°, the Pythagorean theorem applies, so the diagonal is found by taking the square root of the sum of the squared side lengths. This works for any rectangle, no matter how long or wide it is.
When to use it
Use this formula when you need the corner-to-corner distance across a rectangular shape, such as on a screen, a field, a room, or a sheet of paper. It is also useful in geometry problems and in real-life measuring tasks where the diagonal is easier to work with than the sides.
Worked example, step by step
A rectangle has length 8 cm and width 6 cm. Use d = √(l² + w²) Substitute the values: d = √(8² + 6²) Square the numbers: d = √(64 + 36) Add: d = √100 Take the square root: d = 10 cm
Common mistakes to avoid
- adding the length and width instead of squaring them first
- forgetting that the formula gives the diagonal, not the perimeter or area
- mixing up units or leaving the final answer without units
Did You Know?
A rectangle's diagonal is found with the Pythagorean theorem, treating the sides as legs.
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