To find side $ a $ use Pythagorean Theorem:

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

After substituting $h = 5\, \text{cm}$ and $s = 4\, \text{cm}$ we have:

$$ \left( 5\, \text{cm} \right)^{2} + \frac{ a^2 }{ 4 } = \left( 4\, \text{cm} \right)^{2} $$ $$ \frac{ a^2 }{ 4 } = \left( 4\, \text{cm} \right)^{2} - \left( 5\, \text{cm} \right)^{2} $$ $$ \frac{ a^2 }{ 4 } = 16\, \text{cm}^2 - 25\, \text{cm}^2 $$ $$ a^2 = -9\, \text{cm}^2 \cdot 4 $$ $$ a^2 = -36\, \text{cm}^2 $$

This equation has no solution $ \Longrightarrow $ The problem has no solution.

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