Find the side $ a $ of a rhombus if diagonal $d_1 = 31$ and diagonal $d_2 = 13$.
Answer
$a = \frac{\sqrt{ 1130 }}{ 2 }$
Explanation
To find side $ a $ use formula:
$$ d_1^2 + d_2^2 = 4 \cdot a^2 $$After substituting $ d_1 = 31 $ and $ d_2 = 13 $ we have:
$$ 31^2 + 13^2 = 4 \cdot a^2 $$ $$ 961 + 169 = 4 \cdot a^2 $$ $$ 4 \cdot a^2 = 1130 $$ $$ a^2 = \frac{ 1130 }{ 4 } $$ $$ a^2 = \frac{ 565 }{ 2 } $$ $$ a = \sqrt{ \frac{ 565 }{ 2 } } $$$$ a = \frac{\sqrt{ 1130 }}{ 2 } $$This page was created using
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