Find the side $ a $ of an equilateral triangle if incircle radius $r = 457$.
Answer
$a = 914 \sqrt{ 3 }$
Explanation
To find side $ a $ use formula:
$$ r = \dfrac{ \sqrt{ 3 } \cdot a }{ 6 } $$After substituting $ r = 457 $ we have:
$$ 457 = \dfrac{ \sqrt{ 3 } \cdot a }{ 6 } $$ $$ \sqrt{ 3 } \cdot a = 457 \cdot 6 $$ $$ \sqrt{ 3 } \cdot a = 2742 $$ $$ a = \dfrac{ 2742 }{ \sqrt{ 3 } } $$ $$ a = 914 \sqrt{ 3 } $$This page was created using
Equilateral Triangle Calculator