Find the diagonal $ d_1 $ of a rhombus if perimeter $P = 20$ and diagonal $d_2 = 6$.
Answer
$d_1 = 8$
Explanation
STEP 1: find side $ a $
To find side $ a $ use formula:
$$ P = 4 \cdot a $$After substituting $ P = 20 $ we have:
$$ 20 = 4 \cdot a $$ $$ a = \dfrac{ 20 }{ 4 } $$ $$ a = 5 $$STEP 2: find diagonal $ d1 $
To find diagonal $ d1 $ use formula:
$$ d_1^2 + d_2^2 = 4 \cdot a^2 $$After substituting $ d_2 = 6 $ and $ a = 5 $ we have:
$$ d_1 ^ {\,2} + 6^2 = 4 \cdot 5^2 $$ $$ d_1 ^ {\,2} + 36 = 100 $$ $$ d_1 ^ {\,2} = 100 - 36 $$ $$ d_1 ^ {\,2} = 64 $$ $$ d_1 = \sqrt{ 64 } $$$$ d_1 = 8 $$This page was created using
Rhombus Calculator