Question

The floor of a rectangular hall has a perimeter $250m$. If the cost of panting the four walls at the rate of $Rs.10$ per $m^2$ is $Rs.15000$, find the height of the hall.

[Hint: Area of the four walls = Lateral surface area.]

Answer 1

Let length, breadth, and height of the rectangular hall be $lm,bm$ and $hm$ respectively.

Area of four walls $2(lh+bh)$

$=2h(l+b)$

= 2(l + b) h

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

$=250m$

∴ Area of four walls $2(l+b)h=250h{m}^2$

Cost of painting per $m^2$ area $=Rs.10$

Cost of painting $250h{m}^2$ area $=250h\times 10=2500h$

However, it is given that the cost of paining the walls is $Rs15000$.

$\Rightarrow 15000=2500h$
$h=\frac{15000}{2500}$
$\therefore h=6$

Therefore, the height of the hall is $6m$