Find the base diagonal $ d $ of a pyramid if height $h = 66$ and lateral edge $e = 65$.
Answer
Problem has no solutions.
Explanation
To find base diagonal $ d $ use Pythagorean Theorem:
$$ h^2 + \frac{ d^2 }{ 4 } = e^2 $$After substituting $ h = 66 $ and $ e = 65 $ we have:
$$ 66^2 + \frac{ d^2 }{ 4 } = 65^2 $$ $$ \frac{ d^2 }{ 4 } = 65^2 - 66^2 $$ $$ \frac{ d^2 }{ 4 } = 4225 - 4356 $$ $$ d^2 = -131 \cdot 4 $$ $$ d^2 = -524 $$This equation has no solution $ \Longrightarrow $ The problem has no solution.
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