Find the diagonal $ d_2 $ of a rhombus if side $a = 10$ and diagonal $d_1 = 10 \sqrt{ 3 }$.
Answer
$d_2 = 10$
Explanation
To find diagonal $ d2 $ use formula:
$$ d_1^2 + d_2^2 = 4 \cdot a^2 $$After substituting $ d_1 = 10 \sqrt{ 3 } $ and $ a = 10 $ we have:
$$ \left(10 \sqrt{ 3 }\right)^2 + d_2^2 = 4 \cdot 10^2 $$ $$ 300 + d_2^2 = 400 $$ $$ d_2^2 = 400 - 300 $$ $$ d_2^2 = 100 $$ $$ d_2 = \sqrt{ 100 } $$$$ d_2 = 10 $$This page was created using
Rhombus Calculator