We have a floor and a carpet of the dimensions given below.
12 units. 18 units
12 units. 8 units
We want to cover the whole floor with the carpet.
Try to cover the floor with the carpet.
What do you find? Is it possible? Let us discuss the following.
Questions
1) Whose area is greater, floor or carpet?
2) How much area of floor can be covered with this carpet?
3) Can we cover the floor with carpet? How can we do it and find the minimum number of
pieces in which carpet should be cut to cover the floor?
4) Find the perimeter of each piece of carpet?
5) If we want to join two pieces using a tape of width 1 unit, find the length of the tape
required.
6) If price of tape is ₹5 per units. Find the money required to buy the tape.
Answers
Answer:
1) The area of floor and carpet are equal.
2) The area covered by the floor is 96 units².
3) No, the carpet cannot cover the floor completely.
4) The perimeter of first carpet is 40 units and perimeter of second carpet is 28 units.
5) The length of the tape required is 12 units.
6) The money required to buy is Rs. 60
Step-by-step explanation:
1) The shape of floor is square.
Area of square = (side)² = (12)² = 144 units²
The shape of carpet is rectangle.
Area of rectangle = Length × Breadth = 18 × 8 = 144 units²
2) The shape of the carpet is rectangle. The area covered by the carpet in square shape is rectangle.
The area covered by the carpet in floor is:
Area covered = 12 × 8 = 96 units²
3) No, the carpet cannot cover the floor completely. It can only cover partially.
The minimum number of carpets required to cover the floor are two carpets.
In first carpet: 6 units of length is need to be removed from the carpet.
In second carpet: 6 units of length and 4 units of breadth are need to be removed from the carpet.
4) The perimeter of first carpet = 2 (12 + 8) = 2(20) = 40 units
The perimeter of second carpet = 2 (12 + 2) = 2(14) = 28 units
5) The length of the square is 12 units.
Thus, the length of the tape required is 12 units.
6) The money required to buy 12 units of tape is:
12 × 6 = Rs. 60
Answer:
1) The area of floor and carpet are equal.
2) The area covered by the floor is 96 units².
3) No, the carpet cannot cover the floor completely.
4) The perimeter of first carpet is 40 units and perimeter of second carpet is 28 units.
5) The length of the tape required is 12 units.
6) The money required to buy is Rs. 60
Step-by-step explanation:
1) The shape of floor is square.
Area of square = (side)² = (12)² = 144 units²
The shape of carpet is rectangle.
Area of rectangle = Length × Breadth = 18 × 8 = 144 units²
2) The shape of the carpet is rectangle. The area covered by the carpet in square shape is rectangle.
The area covered by the carpet in floor is:
Area covered = 12 × 8 = 96 units²
3) No, the carpet cannot cover the floor completely. It can only cover partially.
The minimum number of carpets required to cover the floor are two carpets.
In first carpet: 6 units of length is need to be removed from the carpet.
In second carpet: 6 units of length and 4 units of breadth are need to be removed from the carpet.
4) The perimeter of first carpet = 2 (12 + 8) = 2(20) = 40 units
The perimeter of second carpet = 2 (12 + 2) = 2(14) = 28 units
5) The length of the square is 12 units.
Thus, the length of the tape required is 12 units.
6) The money required to buy 12 units of tape is:
12 × 5 = Rs. 60