Find the side $ a $ of a rhombus if diagonal $d_1 = \sqrt{ 306 }$ and diagonal $d_2 = \sqrt{ 34 }$.
Answer
$a = \sqrt{ 85 }$
Explanation
To find side $ a $ use formula:
$$ d_1^2 + d_2^2 = 4 \cdot a^2 $$After substituting $ d_1 = \sqrt{ 306 } $ and $ d_2 = \sqrt{ 34 } $ we have:
$$ \left( \sqrt{ 306 } \right)^{ 2 } + \left( \sqrt{ 34 } \right)^{ 2 } = 4 \cdot a^2 $$ $$ 306 + 34 = 4 \cdot a^2 $$ $$ 4 \cdot a^2 = 340 $$ $$ a^2 = \frac{ 340 }{ 4 } $$ $$ a^2 = 85 $$ $$ a = \sqrt{ 85 } $$This page was created using
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