If the length of a side of a rhombus is 36 cm and the area of the rhombus is 396 sq. cm, then the absolute value of the difference between the lengths, in cm, of the diagonals of the rhombus is:
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Correct Answer: 60
Solution and Explanation
Step 2: Use the diagonal–side relationship. Diagonals of a rhombus bisect each other at right angles, so by Pythagoras: \[ \left(\frac{d_1}{2}\right)^2 + \left(\frac{d_2}{2}\right)^2 = a^2. \] Multiply by 4: \[ d_1^2 + d_2^2 = 4a^2 = 4(36^2) = 5184. \]
Step 3: Compute \(|d_1 - d_2|\). Use the identity: \[ (d_1 - d_2)^2 = d_1^2 + d_2^2 - 2 d_1 d_2. \] Substitute known values: \[ (d_1 - d_2)^2 = 5184 - 2(792) = 5184 - 1584 = 3600. \] \[ |d_1 - d_2| = \sqrt{3600} = 60. \] Thus, the required difference between the diagonals is: \[ \boxed{60}. \]
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Note: The figure shown is representative
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