The height of a room is 40% of its semi-perimeter. It Cost Rs. 260 to paper the walls of the room with paper 50 cm wide at the rate of Rs. 2 per m allowing an area of 15 m^2 for doors and Windows. The height of the room is

Explanation:

Let the length, breadth and height of the room be l, b and h respectively.

Then, h = 0.4 (l + b)

Area of the four walls = 2 (l + b)h

= 2 (l + b) × 0.4 (l + b) = 0.8 (l+b)^2

Required area where paper has to be pasted

= 4\5 (l+b)^2 – 15

Now, area of paper = area of wall

Length × breadth = 4\5 (l+b)^2 – 15

Length = 4\5(l+b)^2−15\1\2

Given, 2 [ 4\5(l+b)2−15] × 2 = 260

=> 16\5(l+b)^2 – 60 = 260

=> 16\5(l+b)^2 = 320

=> (l+b)^2 = 100

=> (l+b) = 10

∴ h = 0.4 × 10 = 4 m