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