Find the side $ a $ of an equilateral triangle if incircle radius $r = 10$.
Answer
$a = 20 \sqrt{ 3 }$
Explanation
To find side $ a $ use formula:
$$ r = \dfrac{ \sqrt{ 3 } \cdot a }{ 6 } $$After substituting $ r = 10 $ we have:
$$ 10 = \dfrac{ \sqrt{ 3 } \cdot a }{ 6 } $$ $$ \sqrt{ 3 } \cdot a = 10 \cdot 6 $$ $$ \sqrt{ 3 } \cdot a = 60 $$ $$ a = \dfrac{ 60 }{ \sqrt{ 3 } } $$ $$ a = 20 \sqrt{ 3 } $$This page was created using
Equilateral Triangle Calculator