Find the side $ a $ of a rhombus if diagonal $d_1 = 4$ and diagonal $d_2 = \frac{ 14 }{ 5 }$.
Answer
$a = \frac{\sqrt{ 149 }}{ 5 }$
Explanation
To find side $ a $ use formula:
$$ d_1^2 + d_2^2 = 4 \cdot a^2 $$After substituting $ d_1 = 4 $ and $ d_2 = \frac{ 14 }{ 5 } $ we have:
$$ 4^2 + \left(\frac{ 14 }{ 5 }\right)^2 = 4 \cdot a^2 $$ $$ 16 + \frac{ 196 }{ 25 } = 4 \cdot a^2 $$ $$ 4 \cdot a^2 = \frac{ 596 }{ 25 } $$ $$ a^2 = \frac{ \frac{ 596 }{ 25 } }{ 4 } $$ $$ a^2 = \frac{ 149 }{ 25 } $$ $$ a = \sqrt{ \frac{ 149 }{ 25 } } $$$$ a = \frac{\sqrt{ 149 }}{ 5 } $$This page was created using
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