Question

The length of a room is two times its breadth and three times its height . if the cost of white wash on the 4 wall at Rs. 50 per m² is Rs. 7200, find the cost of carpeting its floor at Rs. 325 per m²​

Answer 1

Explanation:

let the height of the room(h) = x

Length(l) = 3*x = 3x

length = 2 * breadth

breadth(b) = length /2 = 3x/2

Cost of whitewashing the 4 walls = ₹ 7200

Area of 4 walls = 7200 ÷ 50 = 144 m² ------(I)

Area of walls = 2lh + 2bh

= 2*3x*x + 2 *
`(3x)/(2)` * x

= 6x² + 3x²

= 9x²

9x² = 144 {From (I)}

x² = 144/9

x² = 16

x =
`√(16)=√(4*4)`

x = 4 m

height = 4 m

length = 3*4 = 12m

Breadth =
`(3)/(2)*4=3*2=6 \ m`

Area of floor = l*b

= 12 * 6

= 72 m²

Cost of carpeting the floor = 72 * 325 = ₹ 23400