the cost of carpeting a room at rs 90/m2 is rs 7200.if the length had been 5m less the cost would have been rs 3600.find the length and breadth of the room.
Answers
Step-by-step explanation:
Solution :-
Given that
The cost of carpeting a room at Rs.90 per 1 m² = Rs. 7200
Total area of the room
= Total cost / Cost per 1 m²
= 7200/90
= 80 m²
Are of the room = 80 m²
Let the length of the room be l m
Let the breadth of the room be b m
We know that
Area of a rectangle = length × breadth sq.units
Area of the room = lb m²
=> lb = 80 --------(1)
=> b = 80/l -------(2)
Given that
If the length had been 5 m less then the cost would have been = Rs. 3600
Area of the room = 3600/90 = 40 m²
According to the given problem
=> (l-5)b = 40
=> (l-5)(80/l) = 40 (from (1))
=> 80(l-5)/l = 40
=> 80(l-5) = 40l
=> 80 l - 400 = 40 l
=> 80 l -40 l = 400
=> 40 l = 400
=> l = 400/40
=> l = 10 m
Therefore, length = 10 m
From (2)
=> b = 80/10
=> b = 8 m
Therefore, breadth = 8 m
Answer:-
The length and breadth of the room are 10 m and 8 m
Check :-
Length = 10 m
Breadth = 8 m
Area = lb = 10×8 = 80 m²
Total cost of carpeting the room at Rs. 90/m²
=80×90 = Rs. 7200
and
If the length is reduced to 5 m then the new length = 10-5 = 5 m
Area = 5×8 = 40 m²
Total cost of carpeting the room at Rs. 90/m²
=40×90 = Rs. 3600
Verified the given relations in the given problem.
Used formulae:-
→Area of a rectangle is lb sq.units
- l = length
- b = breadth
Step-by-step explanation:
Step-by-step explanation:
Solution :-
Given that
The cost of carpeting a room at Rs.90 per 1 m² = Rs. 7200
Total area of the room
= Total cost / Cost per 1 m²
= 7200/90
= 80 m²
Are of the room = 80 m²
Let the length of the room be l m
Let the breadth of the room be b m
We know that
Area of a rectangle = length × breadth sq.units
Area of the room = lb m²
=> lb = 80 --------(1)
=> b = 80/l -------(2)
Given that
If the length had been 5 m less then the cost would have been = Rs. 3600
Area of the room = 3600/90 = 40 m²
According to the given problem
=> (l-5)b = 40
=> (l-5)(80/l) = 40 (from (1))
=> 80(l-5)/l = 40
=> 80(l-5) = 40l
=> 80 l - 400 = 40 l
=> 80 l -40 l = 400
=> 40 l = 400
=> l = 400/40
=> l = 10 m
Therefore, length = 10 m
From (2)
=> b = 80/10
=> b = 8 m
Therefore, breadth = 8 m
Answer:-
The length and breadth of the room are 10 m and 8 m
Check :-
Length = 10 m
Breadth = 8 m
Area = lb = 10×8 = 80 m²
Total cost of carpeting the room at Rs. 90/m²
=80×90 = Rs. 7200
and
If the length is reduced to 5 m then the new length = 10-5 = 5 m
Area = 5×8 = 40 m²
Total cost of carpeting the room at Rs. 90/m²
=40×90 = Rs. 3600
Verified the given relations in the given problem.
Used formulae:-
→Area of a rectangle is lb sq.units
l = length
b = breadth