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