For a triangle whose sides are $50\, m$,$78\, m$,and $112\, m$ respectively,the length of the perpendicular from the opposite angle to the side $112\, m$ is ......... $m$.

$A$ 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

$A$ person $A$ takes $15 \text{ seconds}$ to cross a rectangular field diagonally walking at a speed of $52 \text{ m/min}$. $A$ person $B$ takes the same time to cross the same field along its sides (length + width) walking at a speed of $68 \text{ m/min}$. The area of the field is $....... \text{ m}^2$.

$A$ rectangular park is $65\, m$ long and $50\, m$ wide. Two cross paths,each $2\, m$ wide,are to be constructed parallel to the sides. If these paths pass through the centre of the rectangle and the cost of construction is ₹ $17.25$ per $m^2$,then find the total cost involved in the construction (in ₹).

If the length and breadth of a rectangular plot are increased by $50 \%$ and $20 \%$ respectively,then the new area is how many times the original area?

An oblong piece of ground measures $19$ $meters$ $2.5$ $dm$ by $12$ $meters$ $5$ $dm$. From the centre of each side,a path $2$ $meters$ wide goes across to the centre of the opposite side. Find the cost of paving these paths at the rate of $Rs.$ $12.32$ per $sq$ $meter$. (in $Rs.$)