To find side $ a $ use formula:

$$ d_1^2 + d_2^2 = 4 \cdot a^2 $$

After substituting $d_1 = 31\, \text{cm}$ and $d_2 = 13\, \text{cm}$ we have:

$$ \left( 31\, \text{cm} \right)^{2} + \left( 13\, \text{cm} \right)^{2} = 4 \cdot a^2 $$ $$ 961\, \text{cm}^2 + 169\, \text{cm}^2 = 4 \cdot a^2 $$ $$ 4 \cdot a^2 = 1130\, \text{cm}^2 $$ $$ a^2 = \frac{ 1130\, \text{cm}^2 }{ 4 } $$ $$ a^2 = \frac{ 565 }{ 2 }\, \text{cm}^2 $$ $$ a = \sqrt{ \frac{ 565 }{ 2 }\, \text{cm}^2 } $$$$ a = \frac{\sqrt{ 1130 }}{ 2 }\, \text{cm} $$

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