# What's the length of the diagonal of a 12 cm x 13 cm x 5 cm rectangular prism to the nearest tenth?

Jun 1, 2018

The length of the diagonal is 18.4 cm.

#### Explanation:

Consider the rectangular prism shown below.

In triangle $\text{ABC}$

${\text{AB"^2 + "BC"^2 = "AC}}^{2}$

In triangle $\text{ACD}$

${\text{AD"^2 = "AC"^2 + "CD"^2 = "AB"^2 + "BC"^2 + "CD}}^{2}$

${\text{AD"^2 = ("13 cm")^2 + ("12 cm")^2 + ("5 cm")^2 = "(169 + 144 + 25) cm"^2 = "338 cm}}^{2}$

$\text{AD" = sqrt("338 cm"^2) = "18.4 cm}$