Find the side $ a $ of a rhombus if diagonal $d_1 = 25$ and diagonal $d_2 = \frac{ 45 }{ 2 }$.
Answer
$a = \frac{ 5 \sqrt{ 181}}{ 4 }$
Explanation
To find side $ a $ use formula:
$$ d_1^2 + d_2^2 = 4 \cdot a^2 $$After substituting $ d_1 = 25 $ and $ d_2 = \frac{ 45 }{ 2 } $ we have:
$$ 25^2 + \left(\frac{ 45 }{ 2 }\right)^2 = 4 \cdot a^2 $$ $$ 625 + \frac{ 2025 }{ 4 } = 4 \cdot a^2 $$ $$ 4 \cdot a^2 = \frac{ 4525 }{ 4 } $$ $$ a^2 = \frac{ \frac{ 4525 }{ 4 } }{ 4 } $$ $$ a^2 = \frac{ 4525 }{ 16 } $$ $$ a = \sqrt{ \frac{ 4525 }{ 16 } } $$$$ a = \frac{ 5 \sqrt{ 181}}{ 4 } $$This page was created using
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