If the length of a rectangular field is increased by $20 \%$ and the breadth is reduced by $20 \%,$ the area of the rectangle will be $192 \, m^2.$ What is the area of the original rectangle? (in $m^2$)

The length of a rectangular plot of ground is four times its breadth and its area is $4$ hectares. How long will it take for a dog to walk around it at the rate of $3\, km/hr$? (in $min$)

$A$ farmer wishes to start a $100 \, m^2$ rectangular vegetable garden. Since he has only $30 \, m$ of barbed wire,he fences three sides of the garden,using his house compound wall as the fourth side. The dimensions of the garden are:

The area of a parallelogram is $72 \, cm^{2}$ and its altitude is twice the corresponding base. The length of the base is.....$cm$.

$D$ and $E$ are points on sides $AB$ and $AC$ of $\Delta ABC$. $DE$ is parallel to $BC$. If $AD:DB = 2:3$,what is the ratio of the area of $\Delta ADE$ to the area of quadrilateral $BDEC$?

The area of a square is $1024\, cm^2$. What is the ratio of the length to the breadth of a rectangle whose length is twice the side of the square and breadth is $12\, cm$ less than the side of this square?