Baudhayan`s theorem, also known as Baudhayan Sulva Sutra, relates to Option 1: Lengths of sides of a right-angled triangle.

Baudhayan was an ancient Indian mathematician and scholar who lived around the 6th century BCE. The Baudhayan Sulva Sutra is a part of the larger Sulva Sutras, which are a collection of texts that deal with various aspects of geometry and mathematics. The Sulva Sutras are a supplement to the Vedas, ancient Indian religious texts.

Baudhayan`s theorem specifically provides a geometric method for constructing right-angled triangles with given side lengths. The theorem states that if the lengths of the two shorter sides of a right-angled triangle are known, the length of the hypotenuse (the longest side) can be determined using a simple geometric construction. The theorem can be represented mathematically as:

c^2 = a^2 + b^2

Where "c" represents the length of the hypotenuse, and "a" and "b" represent the lengths of the other two sides of the right-angled triangle.

This theorem predates the Pythagorean theorem, which is a more well-known and general form of the same concept. The Pythagorean theorem, attributed to the ancient Greek mathematician Pythagoras, states that in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.

The Baudhayan Sulva Sutra provides a practical and geometric approach for constructing right-angled triangles based on given side lengths. It showcases the advanced mathematical knowledge and skills possessed by ancient Indian mathematicians and demonstrates their contributions to the field of geometry.

In summary, Baudhayan`s theorem, or Baudhayan Sulva Sutra, is specifically related to Option 1: Lengths of sides of a right-angled triangle. It provides a geometric construction method for determining the length of the hypotenuse based on the known lengths of the other two sides of a right-angled triangle.