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