Find the side $ a $ of an equilateral triangle if area $A = 1000$.
Answer
$a = 48.0562$
Explanation
To find side $ a $ use formula:
$$ A = \dfrac{ \sqrt{ 3 } \cdot a^2 }{ 4 }$$After substituting $ A = 1000 $ we have:
$$ 1000 = \dfrac{ \sqrt{ 3 } \cdot a^2 }{ 4 }$$ $$ 1000 \cdot 4 = \sqrt{ 3 } \cdot a^2 $$ $$ 4000 = \sqrt{ 3 } \cdot a^2 $$ $$ a^2 = \dfrac{ 4000 }{ \sqrt{ 3 } } $$ $$ a^2 = \frac{ 4000 \sqrt{ 3}}{ 3 } $$ $$ a = \sqrt{ \frac{ 4000 \sqrt{ 3}}{ 3 } } $$$$ a \approx 48.0562 $$This page was created using
Equilateral Triangle Calculator