CAT 2025 Slot 1 QA Question 5: 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

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 $d_{2}$.
$	ext{Area} = \dfrac{d_{1}d_{2}}{2} = 396$
$d_{1}d_{2} = 792$

The diagonals of a rhombus bisect each other at right angles. Hence, half of each diagonal and a side form a right triangle.
${(\dfrac{d_{1}}{2})}^{2} + {(\dfrac{d_{2}}{2})}^{2} =