To find incircle radius $ r $ use formula:
$$ r = \dfrac{ \sqrt{ 3 } \cdot a }{ 2 } $$After substituting $ a = \frac{ 53 }{ 50 } $ we have:
$$ r = \dfrac{ \sqrt{ 3 } \cdot \frac{ 53 }{ 50 } }{ 2 } $$$$ r = \dfrac{ \frac{ 53 \sqrt{ 3}}{ 50 } }{ 2 } $$ $$ r = \frac{ 53 \sqrt{ 3}}{ 100 } $$