STEP 1: find side $ a $

To find side $ a $ use formula:

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

After substituting $d_1 = 14.14\, \text{cm}$ and $d_2 = 5.66\, \text{cm}$ we have:

$$ \left( 14.14\, \text{cm} \right)^{2} + \left( 5.66\, \text{cm} \right)^{2} = 4 \cdot a^2 $$ $$ 199.9396\, \text{cm}^2 + 32.0356\, \text{cm}^2 = 4 \cdot a^2 $$ $$ 4 \cdot a^2 = 231.9752\, \text{cm}^2 $$ $$ a^2 = \frac{ 231.9752\, \text{cm}^2 }{ 4 } $$ $$ a^2 = 57.9938\, \text{cm}^2 $$ $$ a = \sqrt{ 57.9938\, \text{cm}^2 } $$$$ a = 7.6154\, \text{cm} $$

STEP 2: find perimeter $ P $

To find perimeter $ P $ use formula:

$$ P = 4 \cdot a $$

After substituting $a = 7.6154\, \text{cm}$ we have:

$$ P = 4 \cdot 7.6154\, \text{cm} $$ $$ P \approx 30.4615\, \text{cm} $$

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