Question
Find the side $ a $ of an equilateral triangle if incircle radius $r = 9\, \text{cm}$.
Answer
$18 \sqrt{ 3 }\, \text{cm}$
Explanation
To find side $ a $ use formula:
$$ r = \dfrac{ \sqrt{ 3 } \cdot a }{ 6 } $$After substituting $r = 9\, \text{cm}$ we have:
$$ 9\, \text{cm} = \dfrac{ \sqrt{ 3 } \cdot a }{ 6 } $$ $$ \sqrt{ 3 } \cdot a = 9\, \text{cm} \cdot 6 $$ $$ \sqrt{ 3 } \cdot a = 54\, \text{cm} $$ $$ a = \dfrac{ 54\, \text{cm} }{ \sqrt{ 3 } } $$ $$ a = 18 \sqrt{ 3 }\, \text{cm} $$This page was created using
Equilateral Triangle Calculator