CAT 2025 Geometry & Mensuration Question (Hard)

Question

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

Accepted Answer

Let the diagonals of the rhombus be d_1 and d_2 We know that the 2 d_1 d_2 396 implies d_1 d_2 792 For a rhombus with side a 36, the diagonals intersect at right angle. Giving a right-angle triangle with the side as hypotenuse. left 2 right 2 left 2 right 2 a 2 implies 4 36 2 1296 d_1 2 d_2 2 5184 W

CAT 2025

Quantitative

Geometry & Mensuration

Hard

$If the length of a side of a rhombus is 36 cm and the area of the rhombus is 396 sq. cm, then the absolute value of the difference between the lengths, in cm, of the diagonals of the rhombus is$

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