Find the diagonal $ d_1 $ of a rhombus if side $a = 45$ and diagonal $d_2 = \frac{ 75 }{ 2 }$.
Answer
$d_1 = \frac{ 15 \sqrt{ 119}}{ 2 }$
Explanation
To find diagonal $ d1 $ use formula:
$$ d_1^2 + d_2^2 = 4 \cdot a^2 $$After substituting $ d_2 = \frac{ 75 }{ 2 } $ and $ a = 45 $ we have:
$$ d_1 ^ {\,2} + \left(\frac{ 75 }{ 2 }\right)^2 = 4 \cdot 45^2 $$ $$ d_1 ^ {\,2} + \frac{ 5625 }{ 4 } = 8100 $$ $$ d_1 ^ {\,2} = 8100 - \frac{ 5625 }{ 4 } $$ $$ d_1 ^ {\,2} = \frac{ 26775 }{ 4 } $$ $$ d_1 = \sqrt{ \frac{ 26775 }{ 4 } } $$$$ d_1 = \frac{ 15 \sqrt{ 119}}{ 2 } $$This page was created using
Rhombus Calculator