STEP 1: find base diagonal $ d $

To find base diagonal $ d $ use Pythagorean Theorem:

$$ h^2 + \frac{ d^2 }{ 4 } = e^2 $$

After substituting $h = 5\, \text{cm}$ and $e = 15\, \text{cm}$ we have:

$$ \left( 5\, \text{cm} \right)^{2} + \frac{ d^2 }{ 4 } = \left( 15\, \text{cm} \right)^{2} $$ $$ \frac{ d^2 }{ 4 } = \left( 15\, \text{cm} \right)^{2} - \left( 5\, \text{cm} \right)^{2} $$ $$ \frac{ d^2 }{ 4 } = 225\, \text{cm}^2 - 25\, \text{cm}^2 $$ $$ d^2 = 200\, \text{cm}^2 \cdot 4 $$ $$ d^2 = 800\, \text{cm}^2 $$ $$ d = \sqrt{ 800\, \text{cm}^2 } $$$$ d = 20 \sqrt{ 2 }\, \text{cm} $$

STEP 2: find side $ a $

To find side $ a $ use formula:

$$ d = \sqrt{ 2 } \cdot a $$

After substituting $d = 20 \sqrt{ 2 }\, \text{cm}$ we have:

$$ 20 \sqrt{ 2 }\, \text{cm} = \sqrt{ 2 } \cdot a $$ $$ a = \dfrac{ 20 \sqrt{ 2 }\, \text{cm} }{ \sqrt{ 2 } } $$ $$ a = 20\, \text{cm} $$

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