Find the diagonal $ d_1 $ of a rhombus if perimeter $P = 80$ and diagonal $d_2 = 24$.
Answer
$d_1 = 32$
Explanation
STEP 1: find side $ a $
To find side $ a $ use formula:
$$ P = 4 \cdot a $$After substituting $ P = 80 $ we have:
$$ 80 = 4 \cdot a $$ $$ a = \dfrac{ 80 }{ 4 } $$ $$ a = 20 $$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 = 24 $ and $ a = 20 $ we have:
$$ d_1 ^ {\,2} + 24^2 = 4 \cdot 20^2 $$ $$ d_1 ^ {\,2} + 576 = 1600 $$ $$ d_1 ^ {\,2} = 1600 - 576 $$ $$ d_1 ^ {\,2} = 1024 $$ $$ d_1 = \sqrt{ 1024 } $$$$ d_1 = 32 $$This page was created using
Rhombus Calculator