Answer:

option (c) 4 m

Step-by-step explanation:

Given :

• 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 meter ALLOWING an area of 15 m² for door and windows.

To find :

the height of room

Solution :

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

Semi perimeter of the room = (l + b)

Let

the height, h= 2x

then, semi perimeter = 5x

l + b = 5x

Area of 4 walls of the room = lh + bh + lh + bh

= h(l + b + l + b)

= h(2l + 2b)

= 2(l + b) × h

= 2(5x) (2x)

= 20x²

It's also given that the area occupied by doors and windows is 15 m²

so, area to be papered = (20x² – 15) m²

Breadth of the paper = 50 cm = 50/100 m = 0.5 m

Area to be papered = Area of the paper

20x² – 15 = length × 0.5

length = 2(20x² – 15)

length = 40x² – 30

It costs Rs. 260 to paper the walls of the room with paper 50 cm wide at Rs. 2 per meter

2 × (40x² – 30) = 260

80x² – 60 = 260

80x² = 260 + 60

80x² = 320

x² = 320/80

x² = 4

X = √4

x = 2

Height of the room = 2(2) = 4 m