Find the perimeter $ P $ of an equilateral triangle if altitude $h = 15 \sqrt{ 3 }$.
Answer
$P = 90$
Explanation
STEP 1: find side $ a $
To find side $ a $ use formula:
$$ h = \dfrac{ \sqrt{ 3 } \cdot a }{ 2 } $$After substituting $ h = 15 \sqrt{ 3 } $ we have:
$$ 15 \sqrt{ 3 } = \dfrac{ \sqrt{ 3 } \cdot a }{ 2 } $$ $$ \sqrt{ 3 } \cdot a = 15 \sqrt{ 3 } \cdot 2 $$ $$ \sqrt{ 3 } \cdot a = 30 \sqrt{ 3 } $$ $$ a = \dfrac{ 30 \sqrt{ 3 } }{ \sqrt{ 3 } } $$ $$ a = 30 $$STEP 2: find perimeter $ P $
To find perimeter $ P $ use formula:
$$ P = 3 \cdot a $$After substituting $ a = 30 $ we have:
$$ P = 3 \cdot 30 $$ $$ P = 90 $$This page was created using
Equilateral Triangle Calculator