Respuesta :
Answer:
The cost of carpeting the room is Rs 19,200
Step-by-step explanation:
Given as :
The height of the four wall = h = 4 meters
The cost of painting the wall at the rate of rs 15 per square meter = rs 2400
The length of room = L
The breadth of room = b = [tex]\dfrac{2}{3}[/tex] of length
i.e b = [tex]\dfrac{2 L}{3}[/tex]
Let The cost of carpeting the room =rs x
Now, According to question
∵Area of 4 wall = 2 × (Length + breadth)× height
i.e Area = 2 × (L + b)× h
Or, Area = 2 × (L + [tex]\dfrac{2 L}{3}[/tex] )× 4
Or, Area = [tex]\dfrac{40 L}{3}[/tex]
Now,
The cost of painting the wall at the rate of rs 15 per square meter = rs 2400
∴ The cost of painting the 4 wall = [tex]\dfrac{2400}{15}[/tex]
i.e [tex]\dfrac{40 L}{3}[/tex] = 160
Or, L = [tex]\frac{160\times 3}{40}[/tex]
So, length = L = 12 meters
The breadth = b = [tex]\dfrac{2 L}{3}[/tex]
i.e breadth = [tex]\frac{2\times 12}{3}[/tex]
Or, breadth = 8 meters
Again
Area of rectangular room = length × breadh
i.e Area of rectangular room = 12 meters × 8 meters
Or, Area of rectangular room = 96 meters²
Now,
The cost of carpeting the room at rs 200 per meters² = area of room × rate of carpeting
i.e x = 96 meters² × 200 per meters²
Or, x = rs 19,200
So, The cost of carpeting the room = x = rs 19,200
Hence, The cost of carpeting the room is Rs 19,200 Answer
