Pythagoras' Theorem can easily be used to find lengths in right-angled triangles in cuboids.

**Example
**

Find the length of the base diagonal BD of this 3 cm x 4cm x 9 cm cuboid to 3 sig. figs.

Hence find the length of the cuboid's diagonal BH to 3 sig. figs.

**Answer**

Locate the relevant right-angled triangle ABD on the cuboid's base.

Using Pythagoras' Theorem,

BD^{2} = 3^{2} + 9^{2} = 9 + 81 = 90

BD = √90 = **9.49 cm**

Next, we look at triangle HDB, keeping the distance BD as √90 rather than 9.49. This is because, when we square √90 we get exactly 90.

Using Pythagoras' Theorem,

BH^{2} = 4^{2} + (√90)^{2} = 16 + 90 = 106

BH = √106 = **10.3 cm**

**Alternative Method**

An alternative method is to say that:

BH^{2} = HD^{2} + AD^{2} + AB^{2} = 4^{2} + 3^{2} + 9^{2} = 16 + 9 + 81 = 106

BH = √106 = **10.3 cm**