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

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Answer 1 · 2018-06-01T20:52:31

The length of the diagonal is 18.4 cm.

Consider the rectangular prism shown below.

Rectangular prism
(Adapted from Brainly.com)

In triangle $"ABC"$

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

In triangle $"ACD"$

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

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

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