Pythagorean Theorem
- Formula / Rule
- Pythagorean Theorem
- Topic
- Geometry
- Formula
In a right-angled triangle:
$c^2 = a^2 + b^2$
Where $c$ is the hypotenuse (longest side).
Common Pythagorean Triples:
- 3, 4, 5
- 5, 12, 13
- 8, 15, 17
- 7, 24, 25
Related Formulas:
- Diagonal of rectangle: $d = \sqrt{l^2 + b^2}$
- Diagonal of square: $d = a\sqrt{2}$
- When to Use
- Right triangles, distance between two points, diagonal calculations.
- Worked Example
Q: A right triangle has legs 6 and 8. Find hypotenuse.
$c^2 = 6^2 + 8^2 = 36 + 64 = 100$ $c = \textbf{10}$