A school has a hall which is 22 m long and 15.5 m broad. A carpet is laid inside the hall
leaving all around a margin of 75 cm from the walls. Find the area of the carpet and the
area of the strip left uncovered. If the width of the carpet is 82 cm, find its cost at the rate of
rupees 60 per m.
Answers
75 cm = 0.75 m
length of hall = 22 m
therefore, length of carpet = 22 - [(0.75) * 2] = 20.5 m
breadth of hall = 15.5 m
therefore, breadth of carpet 15.5 - [(0.75) * 2] = 14 m
area of hall = 22 * 15.5 = 341 sq. m
area of carpet = 20.5 * 14 = 287 sq. m
area of strip = 341 - 287 = 54 sq. m
length of carpet = 20.5 m
width of carpet = 0.82 m
area of carpet = 20.5 * 0.82 = 16.81 sq. m
cost = area * cost per sq. m
cost = 16.81 * 60
cost = Rs. 1008.6
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Given :-
Length of hall = 22 m
Breadth of hall = 15.5 m
Distance of carpet away from walls = 75 cm
Width of the carpet = 82 cm
Cost of carpet per meter = Rs.60
To Find :-
Area of the carpet.
Area of strip left uncovered.
Cost of carpeting the hall.
Solution :-
We know that,
- l = Length
- b = Breadth
- a = Area
- p = Perimeter
- d = Distance
Given that,
Length of hall (l) = 22 m
Breadth of hall (b) = 15.5 m
Then the area would be,
Substituting their values, we get
Since 100 cm = 1 m
Margin of carpet = 75 cm = 0.75 m
Length of the carpet =
Length of the carpet = 20.5 m
Breadth of the carpet =
Breadth of the carpet = 14 m
We know that,
Area of a rectangle = Length × Breadth
Substituting their values, we get
Substituting their values, we get
Area of 1 m length of the carpet =
Area of 1 m length of the carpet =
∴ Length of the carpet whose area is 287 m² =
Cost of the 350 m long carpet = Rs 60 × 350
Cost of the 350 m long carpet = Rs 21000