the lenght of a room is twice its breadth and thrice its height if the cost of carpeting the floor at rs 80 per sq metre is rs 9000 find the cost of plastering its walls and ceiling at rs 35 per sq metre​

Let's define the variables:

L = length of the room

B = breadth of the room

H = height of the room.

We know that:

L = 2*B

L = 3*H

Remember that the area of a rectangle of length L and breadth B is:

A = L*B

Then the area of the floor of the room is:

A = L*B

and L = 2*B, if we replace that, we get:

A = (2*B)*B

A = 2*B^2

Now, we know that the cost of carpeting the floor is $80 per m^2

And the total cost was $9000

Then the number of square meters in the floor (thus, the area of the floor) is:

A = ($9000)/($80)  m^2

A = 112.5 m^2

With this, we can find the value of B.

A = 112.5 m^2 = 2*B^2

B = √( 112.5/2) m = 7.5 m

Then the length is:

L = 2*B = 2*7.5m = 15m

And the height is:

L = 3*H

H = L/3 = 15m/3 = 5m

Now that we know all the dimensions of the room, we need to find the area of the four walls, and the area of the ceiling (which is equal to the area of the floor 112.5 m^2)

Now, we will have two walls with an area of:

area = breadth*height = B*H = (7.5m)*(5m) = 37.5m^2

And two walls with an area of:

area = length*height = L*H = 75m^2

Then the total area of the four walls plus the ceiling is:

A' = 2*(37.5m^2) + 2*( 75m^2) + 112.5 m^2

A' = 337.5 m^2

And we know that for each m^2, the cost of plastering is $35

Then for 337.5 m^2, the cost will be 337.5 times $35

Cost = (337.5)*$35 = $11,812.50