Question
Find the short base $ b $ of a trapezoid if long base $a = 5\, \text{cm}$, side $c = 2\, \text{cm}$ and height $h = 2\, \text{cm}$.
Answer
Problem has no solutions.
Explanation
To find side $ x $ use Pythagorean Theorem:
$$ h^2 + x^2 = c^2 $$After substituting $h = 2\, \text{cm}$ and $c = 2\, \text{cm}$ we have:
$$ \left( 2\, \text{cm} \right)^{2} + x^2 = \left( 2\, \text{cm} \right)^{2} $$ $$ x^2 = \left( 2\, \text{cm} \right)^{2} - \left( 2\, \text{cm} \right)^{2} $$ $$ x^2 = 4\, \text{cm}^2 - 4\, \text{cm}^2 $$ $$ x^2 = $$This equation has no solution $ \Longrightarrow $ The problem has no solution.
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