The length of a rectangle is increased by $60 \%$. By what percent would the width have to be decreased so as to maintain the same area?

$A$ wire bent in the form of a circle of radius $42 \, cm$ is bent in the form of a rectangle whose sides are in the ratio of $6:5$. The smaller side of the rectangle is (in $cm$)

If the measures of a diagonal and the area of a rectangle are $25\, cm$ and $168\, cm^2$ respectively,what is the length of the rectangle? (in $cm$)

The dimensions of a field are $20 \text{ m}$ by $9 \text{ m}$. $A$ pit $10 \text{ m}$ long,$4.5 \text{ m}$ wide and $3 \text{ m}$ deep is dug in one corner of the field and the earth removed has been evenly spread over the remaining area of the field. What will be the rise in the height of the field as a result of this operation? (in $m$)

An open box is made of wood $2\, cm$ thick. Its internal length is $86\, cm,$ breadth $46\, cm$ and height is $38\, cm.$ The cost of painting the outer surface of the box at $Rs.$ $10$ per $m^2$ is? (in $Rs.$)

$A$ triangle and a parallelogram are constructed on the same base such that their areas are equal. If the altitude of the parallelogram is $100 \, m$,then the altitude of the triangle is