Question : The area of a rhombus is 256 square cm, and one of its diagonals is twice the other in length. The length of its larger diagonal is:
Option 1: 32 cm
Option 2: 16 cm
Option 3: 48 cm
Option 4: 24 cm
Correct Answer: 32 cm
Solution :
Let the first diagonal be $x$ and the second diagonal be $2x$.
Area of rhombus = $\frac{1}{2}\times$(Product of the diagonals)
$256 = \frac{1}{2}\times x \times 2x$
⇒ $256 = x^2$
⇒ $x=16$
So, the length of the larger diagonal = 2 × 16 = 32 cm
Hence, the correct answer is 32 cm.
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