Find the side $ a $ of an equilateral triangle if area $A = 27 \sqrt{ 3 }$.
Answer
$a = 6 \sqrt{ 3 }$
Explanation
To find side $ a $ use formula:
$$ A = \dfrac{ \sqrt{ 3 } \cdot a^2 }{ 4 }$$After substituting $ A = 27 \sqrt{ 3 } $ we have:
$$ 27 \sqrt{ 3 } = \dfrac{ \sqrt{ 3 } \cdot a^2 }{ 4 }$$ $$ 27 \sqrt{ 3 } \cdot 4 = \sqrt{ 3 } \cdot a^2 $$ $$ 108 \sqrt{ 3 } = \sqrt{ 3 } \cdot a^2 $$ $$ a^2 = \dfrac{ 108 \sqrt{ 3 } }{ \sqrt{ 3 } } $$ $$ a^2 = 108 $$ $$ a = \sqrt{ 108 } $$ $$ a = 6 \sqrt{ 3 } $$This page was created using
Equilateral Triangle Calculator