Question

The perimeter of floor of a room is $25$ metres. If the cost of painting the walls of the room is Rs.$750$ at the rate of Rs. $10$ per sq. metre, then find the height of the room.

Answer 1

Let $l$, $b$ and $h$ be the length, breadth and height of the room.

The four walls of the room are to be painted.

Area of the two walls containing the length $=2lh$

Area of the two walls containing the breadth $=2bh$

Total area of four walls$=2lh+2bh$
$=h\times 2(l+b)$

But $2(l+b)$ means the perimeter of the floor of the room.

Total area of walls $=25\times h$ sq.m. ....(i)

Total area of walls $=\frac{\text{Total cost of painting}}{\text{Rate of painting}}$$=\frac{750}{10}$

Total area of walls$=75$sq. m. ...(ii)

Equation (i) $=$ equation (ii)

$25h=75$

$\therefore h=3m$

Thus, the height of the room is $3$m.