Find the altitude $ h $ of an equilateral triangle if perimeter $P = 21$.
Answer
$h = \frac{ 7 \sqrt{ 3}}{ 2 }$
Explanation
STEP 1: find side $ a $
To find side $ a $ use formula:
$$ P = 3 \cdot a $$After substituting $ P = 21 $ we have:
$$ 21 = 3 \cdot a $$ $$ a = \dfrac{ 21 }{ 3 } $$ $$ a = 7 $$STEP 2: find height $ h $
To find height $ h $ use formula:
$$ h = \dfrac{ \sqrt{ 3 } \cdot a }{ 2 } $$After substituting $ a = 7 $ we have:
$$ h = \dfrac{ \sqrt{ 3 } \cdot 7 }{ 2 } $$$$ h = \dfrac{ 7 \sqrt{ 3 } }{ 2 } $$ $$ h = \frac{ 7 \sqrt{ 3}}{ 2 } $$This page was created using
Equilateral Triangle Calculator