Find the side $ a $ of a rhombus if diagonal $d_1 = 9$ and diagonal $d_2 = 5$.
Answer
$a = \frac{\sqrt{ 106 }}{ 2 }$
Explanation
To find side $ a $ use formula:
$$ d_1^2 + d_2^2 = 4 \cdot a^2 $$After substituting $ d_1 = 9 $ and $ d_2 = 5 $ we have:
$$ 9^2 + 5^2 = 4 \cdot a^2 $$ $$ 81 + 25 = 4 \cdot a^2 $$ $$ 4 \cdot a^2 = 106 $$ $$ a^2 = \frac{ 106 }{ 4 } $$ $$ a^2 = \frac{ 53 }{ 2 } $$ $$ a = \sqrt{ \frac{ 53 }{ 2 } } $$$$ a = \frac{\sqrt{ 106 }}{ 2 } $$This page was created using
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