Find the side $ a $ of an equilateral triangle if area $A = 18 \sqrt{ 3 }$.
Answer
$a = 6 \sqrt{ 2 }$
Explanation
To find side $ a $ use formula:
$$ A = \dfrac{ \sqrt{ 3 } \cdot a^2 }{ 4 }$$After substituting $ A = 18 \sqrt{ 3 } $ we have:
$$ 18 \sqrt{ 3 } = \dfrac{ \sqrt{ 3 } \cdot a^2 }{ 4 }$$ $$ 18 \sqrt{ 3 } \cdot 4 = \sqrt{ 3 } \cdot a^2 $$ $$ 72 \sqrt{ 3 } = \sqrt{ 3 } \cdot a^2 $$ $$ a^2 = \dfrac{ 72 \sqrt{ 3 } }{ \sqrt{ 3 } } $$ $$ a^2 = 72 $$ $$ a = \sqrt{ 72 } $$ $$ a = 6 \sqrt{ 2 } $$This page was created using
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