Find the side $ a $ of a rectangle if side $b = 10$ and diagonal $d = 8$.
Answer
Problem has no solutions.
Explanation
To find side $ a $ use Pythagorean Theorem:
$$ a^2 + b^2 = d^2 $$After substituting $ b = 10 $ and $ d = 8 $ we have:
$$ a ^ {\,2} + 10^2 = 8^2 $$ $$ a ^ {\,2} = 8^2 - 10^2 $$ $$ a ^ {\,2} = 64 - 100 $$ $$ a ^ {\,2} = -36 $$This equation has no solution $ \Longrightarrow $ The problem has no solution.
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