Find the face diagonal $ f $ of a cube if body diagonal $d = 5 \sqrt{ 3 }\, \text{cm}$.
Answer
$5 \sqrt{ 2 }\, \text{cm}$
Explanation
STEP 1: find side $ a $
To find side $ a $ use formula:
$$ d = \sqrt{ 3 } \cdot a $$After substituting $d = 5 \sqrt{ 3 }\, \text{cm}$ we have:
$$ 5 \sqrt{ 3 }\, \text{cm} = \sqrt{ 3 } \cdot a $$ $$ a = \dfrac{ 5 \sqrt{ 3 }\, \text{cm} }{ \sqrt{ 3 } } $$ $$ a = 5\, \text{cm} $$STEP 2: find face diagonal $ f $
To find face diagonal $ f $ use formula:
$$ f = \sqrt{ 2 } \cdot a $$After substituting $a = 5\, \text{cm}$ we have:
$$ f = \sqrt{ 2 } \cdot 5\, \text{cm} $$ $$ f = 5 \sqrt{ 2 }\, \text{cm} $$This page was created using
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