STEP 1: find side $ a $

To find side $ a $ use formula:

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

After substituting $d_1 = 16\, \text{cm}$ and $d_2 = 12\, \text{cm}$ we have:

$$ \left( 16\, \text{cm} \right)^{2} + \left( 12\, \text{cm} \right)^{2} = 4 \cdot a^2 $$ $$ 256\, \text{cm}^2 + 144\, \text{cm}^2 = 4 \cdot a^2 $$ $$ 4 \cdot a^2 = 400\, \text{cm}^2 $$ $$ a^2 = \frac{ 400\, \text{cm}^2 }{ 4 } $$ $$ a^2 = 100\, \text{cm}^2 $$ $$ a = \sqrt{ 100\, \text{cm}^2 } $$$$ a = 10\, \text{cm} $$

STEP 2: find perimeter $ P $

To find perimeter $ P $ use formula:

$$ P = 4 \cdot a $$

After substituting $a = 10\, \text{cm}$ we have:

$$ P = 4 \cdot 10\, \text{cm} $$ $$ P = 40\, \text{cm} $$

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