To find side $ a $ use formula:

$$ P = 2 a + 2 b $$

After substituting $P = \dfrac{ 301 }{ 2 }\, \text{cm}$ and $b = \dfrac{ 121 }{ 4 }\, \text{cm}$ we have:

$$ \frac{ 301 }{ 2 }\, \text{cm} = 2 a + 2 \cdot \frac{ 121 }{ 4 }\, \text{cm} $$ $$ \frac{ 301 }{ 2 }\, \text{cm} = 2 a + \frac{ 121 }{ 2 }\, \text{cm} $$ $$ 2 a = \frac{ 301 }{ 2 }\, \text{cm} - \frac{ 121 }{ 2 }\, \text{cm} $$ $$ 2 a = 90\, \text{cm} $$ $$ a = \dfrac{ 90\, \text{cm} }{ 2 } $$ $$ a = 45\, \text{cm} $$

Rectangle Calculator