Question

Question:

A room is half as long again as it is board. The cost of carpeting the room at Rs. 3.25 per m² is Rs 175.50 and the cost of papering the walls at Rs 1.40 per m² is Rs 240.80. If 1 door and 2 windows occupy 8 m² , find the dimensions of the room.

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Answer 1

Given A room is half as long again as it is broad

Let the breadth of the room x m

length of the room x + x/2 = 3x/2m

Area of the room , x × 3x/2 = 3x²/2m

Given , cost of carpeting the room at Rs. 3.25m⁻²

So , total cost , 3x²/2 × 3.25

But , Total cost of carpeting is given as 175.50 so ,

• (3x²/2 )× 3.25 = 175.50
• x² = 175.50 × 2 / 3.25 × 3
• x² = 36
• x = 6

• Breadth x = 6 m
• length 3x/2 = 9m

let the height of the room H m

Area of the four wall = 2(L+ b)× h 2(6+9)× H

= 30H m²

Area of the of the one door and two window is 8m²

8m² Area to be prepared = Area of four wall - area of two window and 1 door = (30H - 8) m²

Given cost of preparing wall is Rs. 1.40m²

total cost of preparing wall is (30H - 8) × 1.40

Total cost of preparing wall is given as 240.80

comparing , (30H - 8 ) × 1.40 = 240.80

• (30H - 8 ) = 240.80 /1.40 = 172
• 30H -. 8 = 172
• 30H = 180
• H = 180/30 = 6

Hence, Dimensions of the room are lengths 9m , breadth 6m and height 6m