Find the side $ a $ of a pyramid if height $h = 6$ and slant height $s = 6$.
Answer
Problem has no solutions.
Explanation
To find side $ a $ use Pythagorean Theorem:
$$ h^2 + \frac{ a^2 }{ 4 } = s^2 $$After substituting $ h = 6 $ and $ s = 6 $ we have:
$$ 6^2 + \frac{ a^2 }{ 4 } = 6^2 $$ $$ \frac{ a^2 }{ 4 } = 6^2 - 6^2 $$ $$ \frac{ a^2 }{ 4 } = 36 - 36 $$ $$ a^2 = 0 \cdot 4 $$ $$ a^2 = 0 $$This equation has no solution $ \Longrightarrow $ The problem has no solution.
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