Find the side $ b $ of a rectangle if side $a = 9$ and diagonal $d = \frac{ 585 }{ 2 }$.
Answer
$b = \frac{ 27 \sqrt{ 469}}{ 2 }$
Explanation
To find side $ b $ use Pythagorean Theorem:
$$ a^2 + b^2 = d^2 $$After substituting $ a = 9 $ and $ d = \frac{ 585 }{ 2 } $ we have:
$$ 9^2 + b^2 = \left(\frac{ 585 }{ 2 }\right)^2 $$ $$ b^2 = \left(\frac{ 585 }{ 2 }\right)^2 - 9^2 $$ $$ b^2 = \frac{ 342225 }{ 4 } - 81 $$ $$ b^2 = \frac{ 341901 }{ 4 } $$ $$ b = \sqrt{ \frac{ 341901 }{ 4 } } $$$$ b = \frac{ 27 \sqrt{ 469}}{ 2 } $$This page was created using
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