CAT (QA) PYQs

If three sides of a rectangular park have a total length $400 \mathrm{ft}$, then the area of the park is maximum when the length (in ft ) of its longer side is

A quadrilateral $A B C D$ is inscribed in a circle such that $A B: C D=2: 1$ and $B C: A D=5: 4$. If $A C$ and $B D$ intersect at the point $E$, then $A E$ : $C E$ equals

ABCD is a trapezium in which AB is parallel to DC, AD is perpendicular to AB, and AB = 3DC. If a circle inscribed in the trapezium touching all the sides has a radius of 3 cm, then the area, in sq. cm, of the trapezium is