Find the side $ a $ of a rhombus if diagonal $d_1 = \frac{ 51 }{ 5 }$ and diagonal $d_2 = \frac{ 93 }{ 10 }$.

$a = \frac{ 3 \sqrt{ 2117}}{ 20 }$

To find side $ a $ use formula:

$$ d_1^2 + d_2^2 = 4 \cdot a^2 $$

After substituting $ d_1 = \frac{ 51 }{ 5 } $ and $ d_2 = \frac{ 93 }{ 10 } $ we have:

$$ \left(\frac{ 51 }{ 5 }\right)^2 + \left(\frac{ 93 }{ 10 }\right)^2 = 4 \cdot a^2 $$ $$ \frac{ 2601 }{ 25 } + \frac{ 8649 }{ 100 } = 4 \cdot a^2 $$ $$ 4 \cdot a^2 = \frac{ 19053 }{ 100 } $$ $$ a^2 = \frac{ \frac{ 19053 }{ 100 } }{ 4 } $$ $$ a^2 = \frac{ 19053 }{ 400 } $$ $$ a = \sqrt{ \frac{ 19053 }{ 400 } } $$$$ a = \frac{ 3 \sqrt{ 2117}}{ 20 } $$

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