# The floor of a rectangular hall has a perimeter 250 m.

Question. The floor of a rectangular hall has a perimeter 250 m. If the cost of panting the four walls at the rate of Rs.10 per m2 is Rs.15000, find the height of the hall.

Solution:

Let length, breadth, and height of the rectangular hall be l m, b m, and h m respectively.

Area of four walls $=2 / h+2 b h$

$=2(I+b) h$

Perimeter of the floor of hall $=2(I+b)$

$=250 \mathrm{~m}$

$\therefore$ Area of four walls $=2(I+b) h=250 h \mathrm{~m}^{2}$

Cost of painting per $\mathrm{m}^{2}$ area $=$ Rs 10

Cost of painting $250 \mathrm{~h} \mathrm{~m}^{2}$ area $=$ Rs $(250 \mathrm{~h} \times 10)=$ Rs $2500 \mathrm{~h}$

However, it is given that the cost of paining the walls is Rs 15000 .

$\therefore 15000=2500 h$

$h=6$

Therefore, the height of the hall is $6 \mathrm{~m}$.