Find the side $ a $ of an equilateral triangle if area $A = 9$.
Answer
$a = 4.559$
Explanation
To find side $ a $ use formula:
$$ A = \dfrac{ \sqrt{ 3 } \cdot a^2 }{ 4 }$$After substituting $ A = 9 $ we have:
$$ 9 = \dfrac{ \sqrt{ 3 } \cdot a^2 }{ 4 }$$ $$ 9 \cdot 4 = \sqrt{ 3 } \cdot a^2 $$ $$ 36 = \sqrt{ 3 } \cdot a^2 $$ $$ a^2 = \dfrac{ 36 }{ \sqrt{ 3 } } $$ $$ a^2 = 12 \sqrt{ 3 } $$ $$ a = \sqrt{ 12 \sqrt{ 3 } } $$$$ a \approx 4.559 $$This page was created using
Equilateral Triangle Calculator