Find the side $ a $ of an equilateral triangle if altitude $h = \sqrt{ 6 }$.
Answer
$a = 2 \sqrt{ 2 }$
Explanation
To find side $ a $ use formula:
$$ h = \dfrac{ \sqrt{ 3 } \cdot a }{ 2 } $$After substituting $ h = \sqrt{ 6 } $ we have:
$$ \sqrt{ 6 } = \dfrac{ \sqrt{ 3 } \cdot a }{ 2 } $$ $$ \sqrt{ 3 } \cdot a = \sqrt{ 6 } \cdot 2 $$ $$ \sqrt{ 3 } \cdot a = 2 \sqrt{ 6 } $$ $$ a = \dfrac{ 2 \sqrt{ 6 } }{ \sqrt{ 3 } } $$ $$ a = 2 \sqrt{ 2 } $$This page was created using
Equilateral Triangle Calculator