Question

The length of a room is 50% more than its breadth. The cost of carpeting the room at the rate of ₹38.50 m² is ₹924 and the cost of papering the walls at ₹3.30 m² is ₹214.50 . If the room has one door of dimensions 1 m × 2 m and two windows each of dimensions 1 m × 1.5 m, find the dimensions of the room. ​

Answer 1

Answer:

Length of the room = 6 meters

Breadth of the room = 4 meters

Height of the room = 3.5 meters

Given:

The length of a room is 50% more than its breadth

The cost of carpeting the room at the rate of ₹ 38.50

The cost of papering the walls at ₹ 3.30 m² is ₹ 214.50

One dimension of the room = 1 m × 2 m

Second dimension of the room = 1 m × 1.5 m

To Find:

The dimensions of the room =?

Answer 2

Answer:

$let \: breadth \: be \: x \\ length = x + x \times \frac{50}{100} = x + \frac{x}{2} = \frac{3x}{2}$

$area \: of \: floor = \frac{924}{38.50} = 24 {m}^{2} \\ area = \frac{3x}{2} \times x \\ 24 = \frac{ {3x}^{2} }{2} \\ {x}^{2} = 24 \times 2 \\ x = \sqrt{64} = 8m$

$breadth = 8m \\ length = 12m$

$let \: height \: be \: h$

$area \: of \: wall = \frac{214.50}{3.30} = 65 {m}^{2} \\ area = 2(12 \times h) + 2(8 \times h)\\ 65 = 24h + 16h \\ 65 = 40h \\ h = \frac{65}{40} = \frac{13}{8}$

$area \: of \: door = 2 {m}^{2} \\ area \: of \: two \: windows = 2 \times 1.5 = 3 {m}^{2}$