Find the side $ a $ of a rhombus if diagonal $d_1 = \frac{ 2497 }{ 10 }$ and diagonal $d_2 = \frac{ 1256 }{ 5 }$.

$a = \frac{\sqrt{ 12545153 }}{ 20 }$

To find side $ a $ use formula:

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

After substituting $ d_1 = \frac{ 2497 }{ 10 } $ and $ d_2 = \frac{ 1256 }{ 5 } $ we have:

$$ \left(\frac{ 2497 }{ 10 }\right)^2 + \left(\frac{ 1256 }{ 5 }\right)^2 = 4 \cdot a^2 $$ $$ \frac{ 6235009 }{ 100 } + \frac{ 1577536 }{ 25 } = 4 \cdot a^2 $$ $$ 4 \cdot a^2 = \frac{ 12545153 }{ 100 } $$ $$ a^2 = \frac{ \frac{ 12545153 }{ 100 } }{ 4 } $$ $$ a^2 = \frac{ 12545153 }{ 400 } $$ $$ a = \sqrt{ \frac{ 12545153 }{ 400 } } $$$$ a = \frac{\sqrt{ 12545153 }}{ 20 } $$

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