STEP 1: find side $ a $

To find side $ a $ use formula:

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

After substituting $d_1 = 18\, \text{cm}$ and $d_2 = 12\, \text{cm}$ we have:

$$ \left( 18\, \text{cm} \right)^{2} + \left( 12\, \text{cm} \right)^{2} = 4 \cdot a^2 $$ $$ 324\, \text{cm}^2 + 144\, \text{cm}^2 = 4 \cdot a^2 $$ $$ 4 \cdot a^2 = 468\, \text{cm}^2 $$ $$ a^2 = \frac{ 468\, \text{cm}^2 }{ 4 } $$ $$ a^2 = 117\, \text{cm}^2 $$ $$ a = \sqrt{ 117\, \text{cm}^2 } $$$$ a = 3 \sqrt{ 13 }\, \text{cm} $$

STEP 2: find perimeter $ P $

To find perimeter $ P $ use formula:

$$ P = 4 \cdot a $$

After substituting $a = 3 \sqrt{ 13 }\, \text{cm}$ we have:

$$ P = 4 \cdot 3 \sqrt{ 13 }\, \text{cm} $$ $$ P = 12 \sqrt{ 13 }\, \text{cm} $$

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