Find the diagonal $ d_1 $ of a rhombus if side $a = 3$ and area $A = 9$.
Answer
Problem has no solutions.
Explanation
STEP 1: find height $ h $
To find height $ h $ use formula:
$$ A = a \cdot h $$After substituting $ A = 9 $ and $ a = 3 $ we have:
$$ 9 = 3 \cdot h $$$$ h = \dfrac{ 9 }{ 3 } $$$$ h = 3 $$STEP 2: find angle $ \alpha $
To find angle $ \alpha $ use formula:
$$ \sin \left( \alpha \right) = \dfrac{ h }{ a } $$After substituting $ h = 3 $ and $ a = 3 $ we have:
$$ \sin \left( \alpha \right) = \dfrac{ 3 }{ 3 } $$ $$ \sin \left( \alpha \right) = 1 $$ $$ \alpha = \arcsin\left( 1 \right) $$ $$ \alpha = 90^o $$Angle $ $ \alpha $ $ has to be lesser than 90 degrees $ \Longrightarrow $ The problem has no solution.
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