Find the side $ a $ of an equilateral triangle if area $A = 36 \sqrt{ 3 }$.
Answer
$a = 12$
Explanation
To find side $ a $ use formula:
$$ A = \dfrac{ \sqrt{ 3 } \cdot a^2 }{ 4 }$$After substituting $ A = 36 \sqrt{ 3 } $ we have:
$$ 36 \sqrt{ 3 } = \dfrac{ \sqrt{ 3 } \cdot a^2 }{ 4 }$$ $$ 36 \sqrt{ 3 } \cdot 4 = \sqrt{ 3 } \cdot a^2 $$ $$ 144 \sqrt{ 3 } = \sqrt{ 3 } \cdot a^2 $$ $$ a^2 = \dfrac{ 144 \sqrt{ 3 } }{ \sqrt{ 3 } } $$ $$ a^2 = 144 $$ $$ a = \sqrt{ 144 } $$ $$ a = 12 $$This page was created using
Equilateral Triangle Calculator