Find the side $ a $ of an equilateral triangle if incircle radius $r = \frac{ 1 }{ 2 }$.
Answer
$a = \sqrt{ 3 }$
Explanation
To find side $ a $ use formula:
$$ r = \dfrac{ \sqrt{ 3 } \cdot a }{ 6 } $$After substituting $ r = \frac{ 1 }{ 2 } $ we have:
$$ \frac{ 1 }{ 2 } = \dfrac{ \sqrt{ 3 } \cdot a }{ 6 } $$ $$ \sqrt{ 3 } \cdot a = \frac{ 1 }{ 2 } \cdot 6 $$ $$ \sqrt{ 3 } \cdot a = 3 $$ $$ a = \dfrac{ 3 }{ \sqrt{ 3 } } $$ $$ a = \sqrt{ 3 } $$This page was created using
Equilateral Triangle Calculator