Find the length of a rope by which a cow must be tethered in order that it may be able to graze an area of $9856 \, m^{2}$. (in $m$)

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 cost of carpeting a room $5 \ m$ wide with carpet at ₹ $3.50$ per $m^2$ is ₹ $105$. The length of the room is ...... $m$.

The length of a rectangular field is double its width. Inside the field,there is a square-shaped pond $8 \, m$ long. If the area of the pond is $\frac{1}{8}$ of the area of the field,what is the length of the field? (in $m$)

If the diameter of each circle is $14 \, cm$ and $DC = CE$,find the area of $\Delta BDE$ in $cm^2$.

The perimeter of a square is $48\, cm$. The area of a rectangle is $4\, cm^2$ less than the area of the square. If the length of the rectangle is $14\, cm$,then its perimeter is.......$cm$.