CAT (QA) PYQs

In a parallelogram $ABCD$ of area $72 \mathrm{sq} \mathrm{cm}$, the sides $CD$ and $AD$ have lengths $9 \mathrm{~cm}$ and $16 \mathrm{~cm}$, respectively. Let P be a point on $C D$ such that $A P$ is perpendicular to $C D$. Then the area, in sq cm, of triangle $A P D$ is

A parallelogram $ABCD$ has area $48 \mathrm{sqcm}$. If the length of CD is $8 \mathrm{~cm}$ and that of $AD$ is s cm , then which one of the following is necessarily true?

The area of a rectangle and the square of its perimeter are in the ratio $1:25$. Then the lengths of the shorter and longer sides of the rectangle are in the ratio