Question

# The dimensions of a room are 8 m×6 m×h. It has two doors each of size 2 m×1 m and one almirah of size 3 m×2 m. The cost of covering the walls by wallpaper which is 40 cm wide at Rs. 1.25 per metre is Rs. 362.50. Find height.

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Solution

## Given: Dimensions of a room are 8 m×6 m×h.Dimensions of the two doors are 2 m×1 mThe dimension of one almirah is 3 m×2 m.Area of the wall to be covered by wallpaper = Area of fours walls − (Area of 2 doors + area of 1 almirah) =2h(8+6)−(2×2×1+3×2) [∵ Area of fours walls = 2×height(length + breadth), area of door = lenght × breadth, Area of almirah = length × breadth)]=28h−10Cost of covering the walls by wallpaper @ Rs. 1.25 per metre =Rs. 362.50Total length of the wallpaper used =Rs. 362.501.25=290 mWidth of the wall paper =40 cm=0.40 mArea of the wallpaper used = (Total length × width) =290×0.40=116 m2Area of the wall to be covered by wallpaper = Area of the wallpaper used28h−10=116⇒28h=116+10⇒h=12628=4.5 mHence, height of the room is 4.5 m.

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