The diagonals of the two faces of the rectangular parallelepiped are 10 cm and 17 cm

The diagonals of the two faces of the rectangular parallelepiped are 10 cm and 17 cm, and the total lateral edge of these faces is 8 cm, find the volume of the parallelepiped.

All faces of a rectangular parallelepiped are rectangles. The diagonals of the faces form right-angled triangles with their sides.

Let us introduce the notation: a, b, c – edges, d1, d2 – diagonals of faces, common edge с = 8 cm.

Let’s compose the equations:

a ^ 2 + c ^ 2 = d1 ^ 2;

b ^ 2 + c ^ 2 = d2 ^ 2.

a ^ 2 = d1 ^ 2 – c ^ 2 = 10 ^ 2 – 8 ^ 2 = 100 – 64 = 36 = 62;

a = 6 cm.

b ^ 2 = d2 ^ 2 – c ^ 2 = 17 ^ 2 – 8 ^ 2 = 289 – 64 = 225 = 152.

b = 15 cm.

The volume of a parallelepiped is equal to the product of its three dimensions:

V = a * b * c = 6 * 15 * 8 = 720 cm2.