A rectangular parallelepiped has dimensions a, b and c express the diagonal d of the rectangular

A rectangular parallelepiped has dimensions a, b and c express the diagonal d of the rectangular parallelepiped through its dimensions.

1. The diagonal of a parallelepiped is the hypotenuse of a rectangular triangle formed by the diagonal of the base, the side of the parallelepiped and the diagonal itself.

2. Consider the base of the parallelepiped and, by the Pythagorean theorem, calculate the diagonal do as the hypotenuse along the two sides of the base a and b, which are legs.

do ^ 2 = a ^ 2 + b ^ 2.

3. Let’s define the diagonal d by two legs, which in this right-angled triangle are the diagonal of the base do and the height c.

d = (do ^ 2 + c ^ 2) ^ 1/2 = {(a ^ 2 + b ^ 2) ^ 2 + c ^ 2} ^ 1/2 =

= (a ^ 4 + 2 * a ^ 2 * b ^ 2 + b ^ 4 + c ^ 2) ^ 1/2.