The area and the length of one of the diagonals of a rhombus is 54 cm2 and 9 cm respectively. Find the length of its other diagonal (in cm).
A) 6 B) 24 C) 12 D) 18
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The area of a parallelogram is a⋅b⋅sinC where a and b are adjacent sides, and C is the angle between them.
Using that, you can use the two side lengths (both equal to 9 cm) and the known area to get the interior angles of the rhombus (one acute, the other obtuse, both with the same sine). Then use the Law of Cosines to get both of the diagonal lengths.
Ans :12 cm.
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