Find the side $ a $ of an equilateral triangle if area $A = \frac{ 39 }{ 2 }$.
Answer
$a = 6.7107$
Explanation
To find side $ a $ use formula:
$$ A = \dfrac{ \sqrt{ 3 } \cdot a^2 }{ 4 }$$After substituting $ A = \frac{ 39 }{ 2 } $ we have:
$$ \frac{ 39 }{ 2 } = \dfrac{ \sqrt{ 3 } \cdot a^2 }{ 4 }$$ $$ \frac{ 39 }{ 2 } \cdot 4 = \sqrt{ 3 } \cdot a^2 $$ $$ 78 = \sqrt{ 3 } \cdot a^2 $$ $$ a^2 = \dfrac{ 78 }{ \sqrt{ 3 } } $$ $$ a^2 = 26 \sqrt{ 3 } $$ $$ a = \sqrt{ 26 \sqrt{ 3 } } $$$$ a \approx 6.7107 $$This page was created using
Equilateral Triangle Calculator