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.)