CAT (QA) PYQs

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

In a trapezium $\mathrm{ABCD}, \mathrm{AB}$ is parallel to $\mathrm{DC}, \mathrm{BC}$ is perpendicular to DC and $\angle \mathrm{BAD}=45^{\circ}$. If $\mathrm{DC}=5 \mathrm{~cm}, \mathrm{BC}=4 \mathrm{~cm}$, the area of the trapezium in sq cm is

Let $ABCD$ be a parallelogram such that the coordinates of its three vertices $A, B, C$ are $(1, 1), (3, 4)$ and $(-2, 8)$, respectively. Then, the coordinates of the vertex $D$ are