Find the side $ a $ of a pyramid if height $h = 5$ and slant height $s = 4$.
Answer
Problem has no solutions.
Explanation
To find side $ a $ use Pythagorean Theorem:
$$ h^2 + \frac{ a^2 }{ 4 } = s^2 $$After substituting $ h = 5 $ and $ s = 4 $ we have:
$$ 5^2 + \frac{ a^2 }{ 4 } = 4^2 $$ $$ \frac{ a^2 }{ 4 } = 4^2 - 5^2 $$ $$ \frac{ a^2 }{ 4 } = 16 - 25 $$ $$ a^2 = -9 \cdot 4 $$ $$ a^2 = -36 $$This equation has no solution $ \Longrightarrow $ The problem has no solution.
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