STEP 1: find side $ a $

To find side $ a $ use formula:

$$ h = \dfrac{ \sqrt{ 3 } \cdot a }{ 2 } $$

After substituting $h = 3\, \text{cm}$ we have:

$$ 3\, \text{cm} = \dfrac{ \sqrt{ 3 } \cdot a }{ 2 } $$ $$ \sqrt{ 3 } \cdot a = 3\, \text{cm} \cdot 2 $$ $$ \sqrt{ 3 } \cdot a = 6\, \text{cm} $$ $$ a = \dfrac{ 6\, \text{cm} }{ \sqrt{ 3 } } $$ $$ a = 2 \sqrt{ 3 }\, \text{cm} $$

STEP 2: find length $ l $

To find length $ l $ use formula:

$$ A = \frac{ a^2 \sqrt{3}}{2} + 3 a l $$

After substituting $A = 30\, \text{cm}$ and $a = 2 \sqrt{ 3 }\, \text{cm}$ we have:

$$ 30\, \text{cm} = \frac{ 2 \sqrt{ 3 }\, \text{cm}^2 \sqrt{3}}{2} + 3 \cdot 2 \sqrt{ 3 }\, \text{cm} \cdot l $$$$ 30\, \text{cm} = \frac{ 12\, \text{cm}^2 \sqrt{3}}{2} + 6 \sqrt{ 3 }\, \text{cm} \cdot l $$$$ 2 \cdot 30\, \text{cm} = 12 \sqrt{ 3 }\, \text{cm}^2 + 2 \cdot 6 \sqrt{ 3 }\, \text{cm} \cdot l $$$$ 60\, \text{cm} = 12 \sqrt{ 3 }\, \text{cm}^2 + 12 \sqrt{ 3 }\, \text{cm} \cdot l $$$$ 12 \sqrt{ 3 }\, \text{cm} \cdot l = 60\, \text{cm} - 12 \sqrt{ 3 }\, \text{cm}^2 $$$$ l = \frac{ 60\, \text{cm} - 12 \sqrt{ 3 }\, \text{cm}^2 }{ 12 \sqrt{ 3 }\, \text{cm} }$$$$ l = \frac{ 39.2154\, \text{cm} }{ 12 \sqrt{ 3 }\, \text{cm} }$$$$ l = 1.8868 $$

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