👉 The math expressed here revolves around a simple yet elegant application of the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. In this context, if we consider a triangle with one side measuring 300 units (the hypotenuse) and the other sides being x and y, the theorem can be written as \(300^2 = x^2 + y^2\). This equation allows us to solve for the unknown side lengths, given the known hypotenuse length. For instance, if we know one of the other sides is 400 units, we can rearrange the equation to find the length of the remaining side: \(y^2 = 300^2 - 400^2\), leading to \(y^2 = 90000 - 160000 = -70000\). However, this result indicates an error in the setup since the square of a real number cannot be negative; thus, this scenario is not physically possible. The correct approach would involve ensuring the given side lengths form a valid right triangle, adhering to the theorem's conditions.
