Find the side $ a $ of a triangular prism if length $l = 5$ and volume $V = 5$.

$a = 1.0746$

To find side $ a $ use formula:

$$ V = \dfrac{ \sqrt{ 3 } \cdot a ^{ 2 } \cdot l }{ 2 } $$

After substituting $ V = 5 $ and $ l = 5 $ we have:

$$ 5 = \dfrac{ \sqrt{ 3 } \cdot a ^{ 2 } \cdot 5 }{ 2 } $$$$ 5 \cdot 2 = \sqrt{ 3 } \cdot a ^{ 2 } \cdot 5 $$$$ 10 = \sqrt{ 3 } \cdot a ^{ 2 } \cdot 5 $$$$ 10 = 5 \sqrt{ 3 } \cdot a ^{ 2 } $$$$ a ^{ 2 } = \dfrac{ 10}{ 5 \sqrt{ 3 } } $$$$ a ^{ 2 } = \frac{ 2 \sqrt{ 3}}{ 3 } $$$$ a = \sqrt{ \frac{ 2 \sqrt{ 3}}{ 3 } } $$$$ a = 1.0746 $$

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