To find side $ a $ use formula:

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

After substituting $d_1 = 32\, \text{cm}$ and $d_2 = 24\, \text{cm}$ we have:

$$ \left( 32\, \text{cm} \right)^{2} + \left( 24\, \text{cm} \right)^{2} = 4 \cdot a^2 $$ $$ 1024\, \text{cm}^2 + 576\, \text{cm}^2 = 4 \cdot a^2 $$ $$ 4 \cdot a^2 = 1600\, \text{cm}^2 $$ $$ a^2 = \frac{ 1600\, \text{cm}^2 }{ 4 } $$ $$ a^2 = 400\, \text{cm}^2 $$ $$ a = \sqrt{ 400\, \text{cm}^2 } $$$$ a = 20\, \text{cm} $$

Rhombus Calculator