Find the side $ a $ of an equilateral triangle if area $A = \frac{ 178 }{ 5 }$.

$a = 9.0672$

To find side $ a $ use formula:

$$ A = \dfrac{ \sqrt{ 3 } \cdot a^2 }{ 4 }$$

After substituting $ A = \frac{ 178 }{ 5 } $ we have:

$$ \frac{ 178 }{ 5 } = \dfrac{ \sqrt{ 3 } \cdot a^2 }{ 4 }$$ $$ \frac{ 178 }{ 5 } \cdot 4 = \sqrt{ 3 } \cdot a^2 $$ $$ \frac{ 712 }{ 5 } = \sqrt{ 3 } \cdot a^2 $$ $$ a^2 = \dfrac{ \frac{ 712 }{ 5 } }{ \sqrt{ 3 } } $$ $$ a^2 = \frac{ 712 \sqrt{ 3}}{ 15 } $$ $$ a = \sqrt{ \frac{ 712 \sqrt{ 3}}{ 15 } } $$$$ a \approx 9.0672 $$

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