CAT 2025 Slot 1 · Quant · Question 15

Let the diagonals be {d}_{1} and {d}_{2}.

Area: \frac{{d}_{1}{d}_{2}}{2}=396, so {d}_{1}{d}_{2}=792.

The diagonals bisect each other at right angles, so the half-diagonals and a side form a right triangle: {\left( \frac{{d}_{1}}{2}\right)}^{2}+{\left( \frac{{d}_{2}}{2}\right)}^{2}={36}^{2}, giving {d}_{1}^{2}+{d}_{2}^{2}=5184.

The question asks for a difference, so build it directly instead of solving for each diagonal:

{\left({d}_{1}-{d}_{2}\right)}^{2}={d}_{1}^{2}+{d}_{2}^{2}-2{d}_{1}{d}_{2}=5184-1584=3600.

So \left|{d}_{1}-{d}_{2}\right|=60 cm.