Find the area $ A $ of a rhombus if side $a = 460$ and diagonal $d_1 = 1000$.
Answer
Problem has no solutions.
Explanation
To find diagonal $ d2 $ use formula:
$$ d_1^2 + d_2^2 = 4 \cdot a^2 $$After substituting $ d_1 = 1000 $ and $ a = 460 $ we have:
$$ 1000^2 + d_2^2 = 4 \cdot 460^2 $$ $$ 1000000 + d_2^2 = 846400 $$ $$ d_2^2 = 846400 - 1000000 $$ $$ d_2^2 = -153600 $$This equation has no solution $ \Longrightarrow $ The problem has no solution.
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