The lenght of a room is twice its bredth and thrice its height . If the cost of carpeting the floor at rs 250sqm is rs 18000. What will be the cost of plastering its four wall at rs 25 persq
Answers
Given :-
The lenght of a room is twice its bredth and thrice its height and the cost of carpeting the floor at rs 250sq.m is rs 18000.
To find :-
What will be the cost of plastering its four wall at rs 25 per sq.m ?
Solution :-
Let the length of the room be (l) = X m
The length of the room = Twice its breadth
=> l = 2b
=> The breadth of the room(b) = l/2
=> X/2 m
The length of the room = Thrice it's height
=> l = 3h
=> h = l/3
=> Height of the room = X/3 m
We know that
Area of the floor = length × breadth
=> Area of the floor = (X)×(X/2)
=> Area of the floor = X²/2 sq.m
Given that:
The cost of carpeting the floor at Rs.250 per sq.m is rs 18000.
Area of the floor = Total cost / Cost per 1 sq.m
=> Area of the floor = 18000/250
=> Area of the floor = 72 sq.m
now, X²/2 = 72
=> X² = 72×2
=> X² = 144
=> X =±√144
=>X = ±12 m
Side can't be negative
So, X = 12 m
Length = 12 m
Breadth = X/2 = 12/2 = 6 m
Height = X/3 = 12/3 = 4 m
We have ,
Length of the room = 12 m
Breadth of the room = 6 m
Height of the room = 4 m
We know that
Area of a four walls of the room in the shape of rectangle = 2h(l+b) sq.units
On Substituting these values
We get,
=> 2(4)(12+6) sq.m
=>2(4)(18) sq.m
=> 144 sq.m
Area of the four walls of the room = 144 sq.m
The cost of plastering the four walls of the roomper 1 sq.m = Rs. 25
Total cost of plastering the fpur walls of the room 144 sq.m
= 144×25
= Rs.3600
Total cost = Rs. 3600
Answer :-
The total cost of plastering the four walls of the room is Rs. 3600
Used formulae:-
Area of the floor = length × breadth sq.units
Area of a four walls of the room in the shape of rectangle = 2h(l+b) sq.units
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