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 ......... $m$.

$A$ room is $7 \text{ m}$ long and $5 \text{ m}$ broad. The doors and windows occupy $5 \text{ m}^2$. The cost of papering the remaining part of the walls with paper $75 \text{ cm}$ wide,at ₹ $4.20$ per piece of $13 \text{ m}$,is ₹ $39.20$. Find the height of the room (in $\text{m}$).

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

The perimeters of a circle,a square,and an equilateral triangle are the same,and their areas are $C$,$S$,and $T$ respectively. Which of the following statements is true?

In measuring the sides of a rectangle,one side is taken $5 \%$ in excess,and the other $4 \%$ in deficit. Find the error percent in the area calculated from these measurements. (in $\%$)

The base of a triangular field is three times its altitude. If the cost of cultivating the field at $50$ per hectare is $Rs. 675$,then what are its base and height?