The Pythagorean Theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. A Pythagorean triplet is a set of three positive integers that satisfy this theorem. For example, the triplet (3, 4, 5) satisfies the theorem since 3^2 + 4^2 = 5^2.


When a square is cut in half diagonally, two right-angled triangles are formed. The hypotenuse of each triangle is a diagonal of the square. If we know the length of a side of the square, we can use the Pythagorean Theorem to calculate the length of the diagonal. Let's use the Pythagorean triplet (3, 4, 5) as an example.

If one side of a square is 8 cm, then the diagonal of the square can be calculated as follows:

- Draw a square with sides of length 8 cm.
- Draw a diagonal line from one corner to the opposite corner of the square.
- Cut the square in half along the diagonal line to create two right-angled triangles.
- Label the sides of the triangle as follows:
- The length of the side opposite the right angle is 8 cm (since it is a side of the square).
- The length of the side adjacent to the right angle is also 8 cm (since the triangle is half of a square).
- The length of the hypotenuse (the diagonal of the square) is unknown and can be denoted by d.
- Use the Pythagorean Theorem to calculate the length of the diagonal:
- d^2 = 8^2 + 8^2
- d^2 = 64 + 64
- d^2 = 128
- d = sqrt(128)
- d = 8sqrt(2)
- Therefore, the length of the diagonal of the square is 8sqrt(2) cm.


In conclusion, the length of the diagonals of a square can be calculated using the Pythagorean Theorem and a Pythagorean triplet. By understanding the relationship between the sides of a right-angled triangle and the diagonal of a square, we can derive a formula for calculating the diagonal length. In this case, the diagonal of a square with sides of length 8 cm is 8sqrt(2) cm.

One diagonal is 11 and other diagonal is also 11