Find the side $ a $ of a rhombus if diagonal $d_1 = 10$ and diagonal $d_2 = 5$.
Answer
$a = \frac{ 5 \sqrt{ 5}}{ 2 }$
Explanation
To find side $ a $ use formula:
$$ d_1^2 + d_2^2 = 4 \cdot a^2 $$After substituting $ d_1 = 10 $ and $ d_2 = 5 $ we have:
$$ 10^2 + 5^2 = 4 \cdot a^2 $$ $$ 100 + 25 = 4 \cdot a^2 $$ $$ 4 \cdot a^2 = 125 $$ $$ a^2 = \frac{ 125 }{ 4 } $$ $$ a^2 = \frac{ 125 }{ 4 } $$ $$ a = \sqrt{ \frac{ 125 }{ 4 } } $$$$ a = \frac{ 5 \sqrt{ 5}}{ 2 } $$This page was created using
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