Write the Pythagorean theorem. For a right-angled triangle with sides a, b and c, let c be the hypotenuse and a and b the other two sides. According to the theorem, c^2 = a^2 + b^2.
Simplify the theorem for a square whose diagonal is the hypotenuse. Because the four sides of squares are equal, the two sides of the triangle formed by hypotenuse as the diagonal are also equal. Therefore, c^2 = a^2 + a^2. That is, c^2 = 2a^2.
Substitute the value of the hypotenuse to calculate the length of the side of the square. For example, suppose the hypotenuse is 6 cm long. Use the formula c^2 = 2a^2. Since 6^2 = 36, and 36/2 = 18, the side of the square equals square root of 18, which equals 4.24.