STEP 1: find side $ a $

To find side $ a $ use formula:

$$ P = 4 \cdot a $$

After substituting $P = 40\, \text{cm}$ we have:

$$ 40\, \text{cm} = 4 \cdot a $$ $$ a = \dfrac{ 40\, \text{cm} }{ 4 } $$ $$ a = 10\, \text{cm} $$

STEP 2: find diagonal $ d2 $

To find diagonal $ d2 $ use formula:

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

After substituting $d_1 = 12\, \text{cm}$ and $a = 10\, \text{cm}$ we have:

$$ \left( 12\, \text{cm} \right)^{2} + d_2^2 = 4 \cdot \left( 10\, \text{cm} \right)^{2} $$ $$ 144\, \text{cm}^2 + d_2^2 = 400\, \text{cm}^2 $$ $$ d_2^2 = 400\, \text{cm}^2 - 144\, \text{cm}^2 $$ $$ d_2^2 = 256\, \text{cm}^2 $$ $$ d_2 = \sqrt{ 256\, \text{cm}^2 } $$$$ d_2 = 16\, \text{cm} $$

Rhombus Calculator