CAT 2025 Slot 1 QA Q15 Geometry

Question 15 of the Quantitative Ability (QA) section, CAT 2025 Slot 1, with CAT's official answer and a worked solution.

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

TITA: type in the answer. There are no options and no negative marking.

Answer: 60 Geometry TITA

Solution

  1. Diagonals \(d_1, d_2\): \(\frac{d_1 d_2}{2} = 396 \Rightarrow d_1 d_2 = 792\).
  2. The half-diagonals and a side form a right triangle: \(d_1^2 + d_2^2 = 4 \times 36^2 = 5184\).
  3. \((d_1 - d_2)^2 = 5184 - 2 \times 792 = 3600 \Rightarrow |d_1 - d_2| = 60\).

Same concept in other years

See every question on Rhombus: side and area give the diagonals via (d1 ± d2)^2.

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