Find the diagonal $ d $ of a rectangle if side $a = \frac{ 27 }{ 500 }$ and side $b = \frac{ 27 }{ 500 }$.
Answer
$d = \frac{ 27 \sqrt{ 2}}{ 500 }$
Explanation
To find diagonal $ d $ use Pythagorean Theorem:
$$ a^2 + b^2 = d^2 $$After substituting $ a = \frac{ 27 }{ 500 } $ and $ b = \frac{ 27 }{ 500 } $ we have:
$$ \left(\frac{ 27 }{ 500 }\right)^2 + \left(\frac{ 27 }{ 500 }\right)^2 = d^2 $$ $$ \frac{ 729 }{ 250000 } + \frac{ 729 }{ 250000 } = d^2 $$ $$ d^2 = \frac{ 729 }{ 125000 } $$ $$ d = \sqrt{ \frac{ 729 }{ 125000 } } $$$$ d = \frac{ 27 \sqrt{ 2}}{ 500 } $$This page was created using
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