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Which mathematical law is given by a²+b²=c²?

  1. Pythagorean theorem

  2. Area of a triangle

  3. Law of Sines

  4. Quadratic equation

The correct answer is: Pythagorean theorem

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b). This relationship can also be written as a²+b²=c². The other options, such as the area of a triangle, are not directly related to the Pythagorean theorem, as they involve different mathematical concepts. The law of Sines also deals with triangles, but it relates ratios of the sides to the sine of the angle opposite the corresponding side. The quadratic equation, on the other hand, is a formula used to solve for the roots of a quadratic function. It is not directly related to the Pythagorean theorem or triangles. Therefore, the correct answer is A Pythagorean theorem.