To find side $ a $ use Pythagorean Theorem:

$$ h^2 + \frac{ a^2 }{ 4 } = s^2 $$

After substituting $h = 13\, \text{cm}$ and $s = 15\, \text{cm}$ we have:

$$ \left( 13\, \text{cm} \right)^{2} + \frac{ a^2 }{ 4 } = \left( 15\, \text{cm} \right)^{2} $$ $$ \frac{ a^2 }{ 4 } = \left( 15\, \text{cm} \right)^{2} - \left( 13\, \text{cm} \right)^{2} $$ $$ \frac{ a^2 }{ 4 } = 225\, \text{cm}^2 - 169\, \text{cm}^2 $$ $$ a^2 = 56\, \text{cm}^2 \cdot 4 $$ $$ a^2 = 224\, \text{cm}^2 $$ $$ a = \sqrt{ 224\, \text{cm}^2 } $$$$ a = 4 \sqrt{ 14 }\, \text{cm} $$

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