Find the diagonal $ d $ of a rectangle if side $a = \frac{ 13 }{ 2 }$ and side $b = 6$.
Answer
$d = \frac{\sqrt{ 313 }}{ 2 }$
Explanation
To find diagonal $ d $ use Pythagorean Theorem:
$$ a^2 + b^2 = d^2 $$After substituting $ a = \frac{ 13 }{ 2 } $ and $ b = 6 $ we have:
$$ \left(\frac{ 13 }{ 2 }\right)^2 + 6^2 = d^2 $$ $$ \frac{ 169 }{ 4 } + 36 = d^2 $$ $$ d^2 = \frac{ 313 }{ 4 } $$ $$ d = \sqrt{ \frac{ 313 }{ 4 } } $$$$ d = \frac{\sqrt{ 313 }}{ 2 } $$This page was created using
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