STEP 1: find side $ a $

To find side $ a $ use formula:

$$ P = 4 \cdot a $$

After substituting $P = 80\, \text{cm}$ we have:

$$ 80\, \text{cm} = 4 \cdot a $$ $$ a = \dfrac{ 80\, \text{cm} }{ 4 } $$ $$ a = 20\, \text{cm} $$

STEP 2: find diagonal $ d1 $

To find diagonal $ d1 $ use formula:

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

After substituting $d_2 = 24\, \text{cm}$ and $a = 20\, \text{cm}$ we have:

$$ d_1 ^ {\,2} + \left( 24\, \text{cm} \right)^{2} = 4 \cdot \left( 20\, \text{cm} \right)^{2} $$ $$ d_1 ^ {\,2} + 576\, \text{cm}^2 = = 1600\, \text{cm}^2 $$ $$ d_1 ^ {\,2} = = 1600\, \text{cm}^2 - 576\, \text{cm}^2 $$ $$ d_1 ^ {\,2} = 1024\, \text{cm}^2 $$ $$ d_1 = \sqrt{ 1024\, \text{cm}^2 } $$$$ d_1 = 32\, \text{cm} $$

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