Find the side $ a $ of a triangular prism if length $l = 7$ and volume $V = 35$.

$a = 2.4028$

To find side $ a $ use formula:

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

After substituting $ V = 35 $ and $ l = 7 $ we have:

$$ 35 = \dfrac{ \sqrt{ 3 } \cdot a ^{ 2 } \cdot 7 }{ 2 } $$$$ 35 \cdot 2 = \sqrt{ 3 } \cdot a ^{ 2 } \cdot 7 $$$$ 70 = \sqrt{ 3 } \cdot a ^{ 2 } \cdot 7 $$$$ 70 = 7 \sqrt{ 3 } \cdot a ^{ 2 } $$$$ a ^{ 2 } = \dfrac{ 70}{ 7 \sqrt{ 3 } } $$$$ a ^{ 2 } = \frac{ 10 \sqrt{ 3}}{ 3 } $$$$ a = \sqrt{ \frac{ 10 \sqrt{ 3}}{ 3 } } $$$$ a = 2.4028 $$

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