Find the area $ A $ of a rhombus if side $a = 8$ and diagonal $d_2 = 17$.
Answer
Problem has no solutions.
Explanation
To find diagonal $ d1 $ use formula:
$$ d_1^2 + d_2^2 = 4 \cdot a^2 $$After substituting $ d_2 = 17 $ and $ a = 8 $ we have:
$$ d_1 ^ {\,2} + 17^2 = 4 \cdot 8^2 $$ $$ d_1 ^ {\,2} + 289 = 256 $$ $$ d_1 ^ {\,2} = 256 - 289 $$ $$ d_1 ^ {\,2} = -33 $$This equation has no solution $ \Longrightarrow $ The problem has no solution.
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