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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.

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Solution

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×2(l+b)

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

Total area of walls =25×h sq.m. ....(i)

Total area of walls =Total cost of paintingRate of painting=75010

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

Equation (i) = equation (ii)

25h=75

h=3m

Thus, the height of the room is 3m.

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