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

1 Answer
Ernest Z.
Jun 1, 2018

The length of the diagonal is 18.4 cm.

Explanation:

Consider the rectangular prism shown below.

Rectangular prism
(Adapted from Brainly.com)

In triangle #"ABC"#

#"AB"^2 + "BC"^2 = "AC"^2#

In triangle #"ACD"#

#"AD"^2 = "AC"^2 + "CD"^2 = "AB"^2 + "BC"^2 + "CD"^2#

#"AD"^2 = ("13 cm")^2 + ("12 cm")^2 + ("5 cm")^2 = "(169 + 144 + 25) cm"^2 = "338 cm"^2#

#"AD" = sqrt("338 cm"^2) = "18.4 cm"#

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