Find the perimeter $ P $ of an equilateral triangle if altitude $h = 24$.
Answer
$P = 48 \sqrt{ 3 }$
Explanation
STEP 1: find side $ a $
To find side $ a $ use formula:
$$ h = \dfrac{ \sqrt{ 3 } \cdot a }{ 2 } $$After substituting $ h = 24 $ we have:
$$ 24 = \dfrac{ \sqrt{ 3 } \cdot a }{ 2 } $$ $$ \sqrt{ 3 } \cdot a = 24 \cdot 2 $$ $$ \sqrt{ 3 } \cdot a = 48 $$ $$ a = \dfrac{ 48 }{ \sqrt{ 3 } } $$ $$ a = 16 \sqrt{ 3 } $$STEP 2: find perimeter $ P $
To find perimeter $ P $ use formula:
$$ P = 3 \cdot a $$After substituting $ a = 16 \sqrt{ 3 } $ we have:
$$ P = 3 \cdot 16 \sqrt{ 3 } $$ $$ P = 48 \sqrt{ 3 } $$This page was created using
Equilateral Triangle Calculator