Find the height $ h $ of a pyramid if slant height $s = 18$ and lateral edge $e = 12$.
Answer
Problem has no solutions.
Explanation
To find side $ a $ use Pythagorean Theorem:
$$ s^2 + \frac{ a^2 }{ 4 } = e^2 $$After substituting $ s = 18 $ and $ e = 12 $ we have:
$$ 18^2 + \frac{ a^2 }{ 4 } = 12^2 $$ $$ \frac{ a^2 }{ 4 } = 12^2 - 18^2 $$ $$ \frac{ a^2 }{ 4 } = 144 - 324 $$ $$ a^2 = -180 \cdot 4 $$ $$ a^2 = -720 $$This equation has no solution $ \Longrightarrow $ The problem has no solution.
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