Find the side $ a $ of an equilateral triangle if area $A = 49 \sqrt{ 3 }$.
Answer
$a = 14$
Explanation
To find side $ a $ use formula:
$$ A = \dfrac{ \sqrt{ 3 } \cdot a^2 }{ 4 }$$After substituting $ A = 49 \sqrt{ 3 } $ we have:
$$ 49 \sqrt{ 3 } = \dfrac{ \sqrt{ 3 } \cdot a^2 }{ 4 }$$ $$ 49 \sqrt{ 3 } \cdot 4 = \sqrt{ 3 } \cdot a^2 $$ $$ 196 \sqrt{ 3 } = \sqrt{ 3 } \cdot a^2 $$ $$ a^2 = \dfrac{ 196 \sqrt{ 3 } }{ \sqrt{ 3 } } $$ $$ a^2 = 196 $$ $$ a = \sqrt{ 196 } $$ $$ a = 14 $$This page was created using
Equilateral Triangle Calculator