CAT (QA) PYQs

Let $A B C$ be a right-angled triangle with $B C$ as the hypotenuse. Lengths of $A B$ and AC are $15 \mathrm{~km}$ and $20 \mathrm{krn}$, respectively. The minimum possible time, in minutes, required to reach the hypotenuse from A at a speed of $30 \mathrm{~km}$ per hour is

In a triangle $ABC$ , medians $AD$ and $BE$ are perpendicular to each other, and have lengths $12 \mathrm{~cm}$ and $9 \mathrm{~cm}$, respectively. Then, the area of triangle $ABC$, in sq cm, is

Let $P$ be an interior point of a right-angled isosceles triangle $ABC$ with hypotenuse $AB$ . If the perpendicular distance of P from each of $A B, B C$, and $C A$ is $4(\sqrt{2}-1) \mathrm{cm}$, then the area, in sq cm, of the triangle $A B C$ is