Find the side $ a $ of an equilateral triangle if area $A = \frac{ 693 }{ 100 }$.

$a = 4.0005$

To find side $ a $ use formula:

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

After substituting $ A = \frac{ 693 }{ 100 } $ we have:

$$ \frac{ 693 }{ 100 } = \dfrac{ \sqrt{ 3 } \cdot a^2 }{ 4 }$$ $$ \frac{ 693 }{ 100 } \cdot 4 = \sqrt{ 3 } \cdot a^2 $$ $$ \frac{ 693 }{ 25 } = \sqrt{ 3 } \cdot a^2 $$ $$ a^2 = \dfrac{ \frac{ 693 }{ 25 } }{ \sqrt{ 3 } } $$ $$ a^2 = \frac{ 231 \sqrt{ 3}}{ 25 } $$ $$ a = \sqrt{ \frac{ 231 \sqrt{ 3}}{ 25 } } $$$$ a \approx 4.0005 $$

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