The Pythagorean theorem is a mathematical relationship that states that in a right triangle (a triangle with one 90-degree angle), the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. This relationship is expressed in the formula:

a^2 + b^2 = c^2

where c is the hypotenuse and a and b are the other two sides.

The Pythagorean theorem can be used to find the length of the hypotenuse of a right triangle if the lengths of the other two sides are known. It can also be used to check whether a set of three numbers could represent the sides of a right triangle.

For example, suppose we have a right triangle with sides of length 3 and 4. We can use the Pythagorean theorem to find the length of the hypotenuse:

Therefore, the length of the hypotenuse of this right triangle is 5.

The Pythagorean theorem is a fundamental concept in geometry and has many practical applications in various fields, such as architecture, construction, and engineering.

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