Find the side $ a $ of a rhombus if diagonal $d_1 = \frac{ 56 }{ 5 }$ and diagonal $d_2 = \frac{ 42 }{ 5 }$.
Answer
$a = 7$
Explanation
To find side $ a $ use formula:
$$ d_1^2 + d_2^2 = 4 \cdot a^2 $$After substituting $ d_1 = \frac{ 56 }{ 5 } $ and $ d_2 = \frac{ 42 }{ 5 } $ we have:
$$ \left(\frac{ 56 }{ 5 }\right)^2 + \left(\frac{ 42 }{ 5 }\right)^2 = 4 \cdot a^2 $$ $$ \frac{ 3136 }{ 25 } + \frac{ 1764 }{ 25 } = 4 \cdot a^2 $$ $$ 4 \cdot a^2 = 196 $$ $$ a^2 = \frac{ 196 }{ 4 } $$ $$ a^2 = 49 $$ $$ a = \sqrt{ 49 } $$$$ a = 7 $$This page was created using
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