The diagonals of the faces of the rectangular parallelepiped are 11cm, 19cm, 20cm. Find the diagonal of the parallelepiped.

It is known from the condition that the diagonals of the faces of the rectangular parallelepiped are 11 cm, 19 cm, 20 cm. In order to find the diagonal of the parallelepiped, we use the property.

The square of the length of the diagonal of a rectangular parallelepiped is equal to the sum of the squares of its edges.

Let us denote by a, b and c – the edges of the parallelepiped.

Let d₁, d₂ and d₃ be the diagonals of the faces of the parallelepiped.

d is the diagonal of the parallelepiped.

Looking for the diagonals of the faces:

d₁ ^ 2 = a ^ 2 + b ^ 2 = 11 ^ 2 = 121;

d₂² = a ^ 2 + c ^ 2 = 19 ^ 2 = 361;

d₃² = b ^ 2 + c ^ 2 = 20 ^ 2 = 400.

We find the sum of three equalities:

2 * a ^ 2 + 2 * b ^ 2 + 2 * c ^ 2 = 2 * d ^ 2 = 882;

a ^ 2 + b ^ 2 + c ^ 2 = 441;

D = 22.