Find the diagonal $ d_2 $ of a rhombus if perimeter $P = 40$ and diagonal $d_1 = 12$.
Answer
$d_2 = 16$
Explanation
STEP 1: find side $ a $
To find side $ a $ use formula:
$$ P = 4 \cdot a $$After substituting $ P = 40 $ we have:
$$ 40 = 4 \cdot a $$ $$ a = \dfrac{ 40 }{ 4 } $$ $$ a = 10 $$STEP 2: find diagonal $ d2 $
To find diagonal $ d2 $ use formula:
$$ d_1^2 + d_2^2 = 4 \cdot a^2 $$After substituting $ d_1 = 12 $ and $ a = 10 $ we have:
$$ 12^2 + d_2^2 = 4 \cdot 10^2 $$ $$ 144 + d_2^2 = 400 $$ $$ d_2^2 = 400 - 144 $$ $$ d_2^2 = 256 $$ $$ d_2 = \sqrt{ 256 } $$$$ d_2 = 16 $$This page was created using
Rhombus Calculator