The total cost of papering the 4 walls is Rs. 1104
Step-by-step explanation:
The given is:
- The length of a room is 3 times its breadth
- Its height is 4.6 m
- The total cost of carpeting the floor of a room at the rate of Rs. 60 per square meter is Rs. 4500
We need to find the total cost of papering the 4 walls at the rate of Rs. 6
Assume that the breadth of the room is x m
∵ The length of the room is 3 times its breadth
∵ The breadth of the room is x m
∴ The length of the room is 3 x m
∵ The floor of the room is shaped a rectangle
- Area of the rectangle = length × breadth
∴ The area of the floor = (3 x) × (x) = 3 x²
∵ The rate of the carpeting is Rs. 60 per square meter
- Multiply the area of the floor by 60 to find the total cost of carpeting
∴ The total cost of carpeting = 3 x²(60) = 180 x²
∵ The total cost of carpeting the floor is Rs. 4500
- Equate the two sides of total cost to find x
∴ 180 x² = 4500
- Divide both sides by 180
∴ x² = 25
- Take √ for both sides
∴ x = 5
∴ The breadth of the room = 5 m
∵ The length of the room is 3 x
∴ The length of the room = 3(5) = 15 m
The four walls of the room has dimensions length × height , breadth × height , length × height , breadth × height ⇒ (each two opposite walls have same dimensions)
∵ The length = 15 m , breadth = 5 m , height = 4.6 m
∴ The area of the four walls = 2(15 × 4.6) + 2(5 × 4.6)
∴ The area of the four walls = 138 + 46
∴ The area of the four walls = 184 m²
∵ The rate per meter square of papering is Rs. 6
- Multiply the area of the four walls by 6 to find the total cost
of papering
∴ The total cost of papering = 184 × 6
∴ The total cost of papering = Rs. 1104
The total cost of papering the 4 walls is Rs. 1104
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