On decreasing each side of an equilateral triangle by $2\, cm$,there is a decrease of $4\sqrt{3}\, cm^2$ in its area. The length of each side of the triangle is.........$cm$.

If the area of an equilateral triangle is equal to the area of an isosceles triangle whose base and equal sides are $16 \, cm$ and $10 \, cm$ respectively,then the side of the equilateral triangle is......$cm$

$A$ playground is in the shape of a rectangle. $A$ sum of ₹ $1,000$ was spent to make the ground usable at the rate of $25$ $paisa$ per $m^2$. The breadth of the ground is $50\, m$. If the length of the ground is increased by $20\, m$,what will be the expenditure in rupees at the same rate per $m^2$?

The length of a rectangular plot is thrice of its breadth. If the area of the rectangular plot is $7803 \ m^2$,what is the breadth of the rectangular plot? (in $m$)

Length of a rectangle is twice of its breadth. Area of the rectangle is $18 \, m^{2}$. What would be its perimeter? (in $m$)

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 $m$)