STEP 1: find side $ a $

To find side $ a $ use formula:

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

After substituting $h = 21\, \text{cm}$ we have:

$$ 21\, \text{cm} = \dfrac{ \sqrt{ 3 } \cdot a }{ 2 } $$ $$ \sqrt{ 3 } \cdot a = 21\, \text{cm} \cdot 2 $$ $$ \sqrt{ 3 } \cdot a = 42\, \text{cm} $$ $$ a = \dfrac{ 42\, \text{cm} }{ \sqrt{ 3 } } $$ $$ a = 14 \sqrt{ 3 }\, \text{cm} $$

STEP 2: find perimeter $ P $

To find perimeter $ P $ use formula:

$$ P = 3 \cdot a $$

After substituting $a = 14 \sqrt{ 3 }\, \text{cm}$ we have:

$$ P = 3 \cdot 14 \sqrt{ 3 }\, \text{cm} $$ $$ P = 42 \sqrt{ 3 }\, \text{cm} $$

Equilateral Triangle Calculator