STEP 1: find side $ a $

To find side $ a $ use formula:

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

After substituting $d_1 = 17\, \text{cm}$ and $d_2 = 8\, \text{cm}$ we have:

$$ \left( 17\, \text{cm} \right)^{2} + \left( 8\, \text{cm} \right)^{2} = 4 \cdot a^2 $$ $$ 289\, \text{cm}^2 + 64\, \text{cm}^2 = 4 \cdot a^2 $$ $$ 4 \cdot a^2 = 353\, \text{cm}^2 $$ $$ a^2 = \frac{ 353\, \text{cm}^2 }{ 4 } $$ $$ a^2 = \frac{ 353 }{ 4 }\, \text{cm}^2 $$ $$ a = \sqrt{ \frac{ 353 }{ 4 }\, \text{cm}^2 } $$$$ a = \frac{\sqrt{ 353 }}{ 2 }\, \text{cm} $$

STEP 2: find perimeter $ P $

To find perimeter $ P $ use formula:

$$ P = 4 \cdot a $$

After substituting $a = \dfrac{\sqrt{ 353 }}{ 2 }\, \text{cm}$ we have:

$$ P = 4 \cdot \frac{\sqrt{ 353 }}{ 2 }\, \text{cm} $$ $$ P = 2 \sqrt{ 353 }\, \text{cm} $$

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