CAT (QA) PYQs

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

Let $D$ and $E$ be points on sides $A B$ and $A C$, respectively, of a triangle $A B C$, such that $A D: B D=2: 1$ and $A E: C E=2: 3$. If the area of the triangle $A D E$ is $8 \mathrm{ sq } \mathrm{cm}$, then the area of the triangle $ABC$ , in sq cm , is

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