The lengths of the diagonals of the three sides of the rectangular parallelepiped having a common vertex are equal

The lengths of the diagonals of the three sides of the rectangular parallelepiped having a common vertex are equal to 7cm 2√17cm and 9cm. Find the diagonal of the box.

To begin with, let’s draw a rectangular parallelepiped in which we denote the lengths of the diagonals of three faces with a common vertex as 7 cm, 2√17 cm and 9 cm.

Let’s take that the length of the parallelepiped is a, the width is x, and the height is c.

Then √a ^ 2 + x ^ 2 = 7, √a ^ 2 + c ^ 2 = 2√17, and √x ^ 2 + c ^ 2 = 9.

Then the diagonal is equal to: √a ^ 2 + x ^ 2 + c ^ 2 = √61 cm.

Then our answer: √61 cm.