To find side $ a $ use formula:

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

After substituting $d_1 = 8\, \text{cm}$ and $d_2 = 15\, \text{cm}$ we have:

$$ \left( 8\, \text{cm} \right)^{2} + \left( 15\, \text{cm} \right)^{2} = 4 \cdot a^2 $$ $$ 64\, \text{cm}^2 + 225\, \text{cm}^2 = 4 \cdot a^2 $$ $$ 4 \cdot a^2 = 289\, \text{cm}^2 $$ $$ a^2 = \frac{ 289\, \text{cm}^2 }{ 4 } $$ $$ a^2 = \frac{ 289 }{ 4 }\, \text{cm}^2 $$ $$ a = \sqrt{ \frac{ 289 }{ 4 }\, \text{cm}^2 } $$$$ a = \frac{ 17 }{ 2 }\, \text{cm} $$

Rhombus Calculator