CAT (QA) PYQs

From an interior point of an equilateral triangle, perpendiculars are drawn on all three sides. The sum of the lengths of the three perpendiculars is $s$. Then the area of triangle is

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

A triangle $ABC$ has area $32$ sq units and its side $BC$ , of length $8$ units, lies on the line $\mathrm{x}=4$. Then the shortest possible distance between $A$ and the point $(0,0)$ is