To find incircle radius $ r $ use formula:
$$ r = \dfrac{ \sqrt{ 3 } \cdot a }{ 2 } $$After substituting $ a = \frac{ 7 }{ 8 } $ we have:
$$ r = \dfrac{ \sqrt{ 3 } \cdot \frac{ 7 }{ 8 } }{ 2 } $$$$ r = \dfrac{ \frac{ 7 \sqrt{ 3}}{ 8 } }{ 2 } $$ $$ r = \frac{ 7 \sqrt{ 3}}{ 16 } $$