Geometry

Pythagorean Theorem

Formula

a² + b² = c²

What is Pythagorean Theorem?

In a right-angled triangle, the square of the hypotenuse equals the sum of the squares of the other two sides. This is one of the most fundamental theorems in geometry.

Variables

a
a — One leg of the right triangle
b
b — The other leg of the right triangle
c
c — The hypotenuse (longest side)

Worked Examples

Example 1

Find the hypotenuse when a = 3 and b = 4.

Solution:

c² = 3² + 4² = 9 + 16 = 25. c = √25 = 5

Example 2

Find side b when a = 6 and c = 10.

Solution:

b² = c² − a² = 100 − 36 = 64. b = 8

Frequently Asked Questions

Related Formulas

Area of a Circle

A = π × r²

Circumference of a Circle

C = 2 × π × r

Area of a Rectangle

A = l × w

Area of a Triangle

A = ½ × b × h

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