Find the diagonal $ d_2 $ of a rhombus if side $a = 12$ and diagonal $d_1 = 12 \sqrt{ 3 }$.
Answer
$d_2 = 12$
Explanation
To find diagonal $ d2 $ use formula:
$$ d_1^2 + d_2^2 = 4 \cdot a^2 $$After substituting $ d_1 = 12 \sqrt{ 3 } $ and $ a = 12 $ we have:
$$ \left(12 \sqrt{ 3 }\right)^2 + d_2^2 = 4 \cdot 12^2 $$ $$ 432 + d_2^2 = 576 $$ $$ d_2^2 = 576 - 432 $$ $$ d_2^2 = 144 $$ $$ d_2 = \sqrt{ 144 } $$$$ d_2 = 12 $$This page was created using
Rhombus Calculator