The ratio of height of a room to its semi-perimeter is 2 : 5. It costs Rs. 260 to paper the walls of the room with paper 50 cm wide at Rs. 2 per metre allowing an area of 15 sq. m for doors and windows. The height of the room is:

4 m

We have,

Total cost = 260 rupees

Per meter cost = 2 rupees

Now the length of the paper = \(\frac{260}{2}\) = 130 meters

Now the area of the paper = 130 × \(\frac{50}{100}\) = 65 m²

Let the height = 2x

and semi perimeter = 5x

Now, Total area of four walls = 15 + 65 = 80 m²

According to the formula = 2 ( l + b ) = 80 m²

2 × 5x × 2x = 80 m²

20 x² = 80

x = 2

Now the height = 2x = 4