# Applying Pythagoras’ Theorem in 3-D

**The longest diagonal in a cuboid**

Pythagoras’ Theorem can also be used to solve three-dimensional problems. For example, find the length of the longest diagonal in a cuboid measuring 5 cm by 7 cm by 8 cm.

The first step would be to label the vertices of the cuboid to determine the longest diagonals. In the example above, CE is the hypotenuse of the right-angled triangle for ACE.

The first step is to find the length go AC.

AC² = 5² + 7²

AC² = 25 + 49

AC² = 74

The second step is to work out CE as AC has already been calculated:

CE² = AE² + AC²

CE² = 8² + 74

CE² = 64 + 74

CE = 11.75 cm (to 2 d.p.)