Question

Hey Friends ☺
☆challenging question ☆

The ratio of a height and semiperimeter of a room is 2 : 5 . At the rate of Rs 2 per meter , the cost of wallpaper having breadth 50 m is Rs 260 . The area occupied by door and Windows is 15 m^2 Find the height of the room

#Answer correctly

Answer 1

hey dear!! :)
let height be 2x metres and (l+b) = 5x metres
length = total cost / rate = 260/2 = 130
area = 130*50/100 = 65 m square
total area of 4 walls = 65 +15 = 80 m sq
2(l+b)*h = 80
2*5x *2x = 80
x sq = 80/20
x = √4
x = 2
so height = 2 *2 = 4 m :)

Answer 2

Method - 1:

Let the common ratio be x.

Given that height of a room = 2x.

Semi-Perimeter of a room (l + b) = 5x.

We know that Area of the 4 walls = 2(l + b) * h

                                                         = 2 * 5x * 2x

                                                          = 20x^2.


Given that Area occupied by door and windows is 15m^2.

Therefore the area to be covered = (20x^2 - 15) cm^2.

Given that At the rate of 2 per meter, the cost of wallpaper having breadth 50m is 260.

2(20x^2 - 15) * 2

4(20x^2 - 15)cm^2.

Now,

4(20x^2 - 15) = 260

20x^2 - 15 = 260/4

20x^2 - 15 = 65

20x^2 = 65 + 15

20x^2 =  80

x^2 = 4

x = 2.


Therefore the height of the room = 2 * 2

                                                         = 4m.





Method:2

Given the height of a room = 2x.

Given semiperimeter of a room = 5x.

Given that the cost of wallpaper at the rate of 2 per meter = 260.

Paper length = 260/2

                       = 130m.


Given Breadth = 50.m

Therefore the total paper required  = 130 * 50

                                                          = 6500.


Therefore the total area covered = (15+ 6500)

                                                         = 6515.


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

             2 * 5x * 2x = 6515

             20x^2 = 6515

             x^2 = 6515/20

            x^2 = 325.75

           x = 18.04


Therefore the height of the room = 2(18.04)

                                                        = ~36.

Its not possible.



So, 

Given breadth should be 50cm.

Therefore the total paper required = 130 * 50/100

                                                          = 65


Therefore the total area covered = 65 + 15

                                                        = 80m^2.




Area of the 4 walls of the room = 2(l + b) * h

                           80 = 2 * 2x * 5x

                            80 = 20x^2

                              4 = x^2

                              2 = x.



Therefore the height of the room = 2 * 2

                                                         = 4m.



NOTE: I took help from one of my friends to solve this.sorry for that

Hope this helps!