Find the perimeter $ P $ of an equilateral triangle if area $A = 307$.

$P = 79.8804$

STEP 1: find side $ a $

To find side $ a $ use formula:

$$ A = \dfrac{ \sqrt{ 3 } \cdot a^2 }{ 4 }$$

After substituting $ A = 307 $ we have:

$$ 307 = \dfrac{ \sqrt{ 3 } \cdot a^2 }{ 4 }$$ $$ 307 \cdot 4 = \sqrt{ 3 } \cdot a^2 $$ $$ 1228 = \sqrt{ 3 } \cdot a^2 $$ $$ a^2 = \dfrac{ 1228 }{ \sqrt{ 3 } } $$ $$ a^2 = \frac{ 1228 \sqrt{ 3}}{ 3 } $$ $$ a = \sqrt{ \frac{ 1228 \sqrt{ 3}}{ 3 } } $$$$ a \approx 26.6268 $$

STEP 2: find perimeter $ P $

To find perimeter $ P $ use formula:

$$ P = 3 \cdot a $$

After substituting $ a = 26.6268 $ we have:

$$ P = 3 \cdot 26.6268 $$ $$ P \approx 79.8804 $$

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