The breadth of a rectangular plot is $75 \%$ of its length. If the perimeter of the plot is $1050 \, m,$ what is its area (in $, m^2$)?

$A$ copper sphere of diameter $18\, cm$ is drawn into a wire of diameter $40\, mm$. Then,the length of the wire is......$cm$?

In $\triangle ABC$,$\angle A = 90^{\circ}$ and $AD \perp BC$,where $D$ lies on $BC$. If $BC = 8 \ cm$ and $AC = 6 \ cm$,then the ratio of the area of $\triangle ABC$ to the area of $\triangle ACD$ is:

The sides of a triangle are in the ratio of $\frac{1}{2}: \frac{1}{3}: \frac{1}{4}$. If the perimeter is $52 \text{ cm}$,then the length of the smallest side is ........ $\text{cm}$.

The length of a rectangle is twice its breadth. If its length is decreased by $5\, cm$ and breadth is increased by $5\, cm$,the area of the rectangle is increased by $75\, cm^2$. Then the length of the rectangle is......$cm$.

$ABCD$ is a trapezium in which $AB \parallel CD$ and $AB = 2CD$. If its diagonals intersect each other at $O$,the ratio of the area of triangle $AOB$ and $COD$ is