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