What is the least number of square pieces into which a cardboard, 13ft long and 8ft wide can be cut?
(With solution pls...) tnx...
What is the size of each square piece? If the square is 8 by 8, then only one can be cut.
To determine the least number of square pieces into which a cardboard measuring 13ft long and 8ft wide can be cut, we need to find the greatest common divisor (GCD) of the two dimensions.
Step 1: Find the GCD of 13ft and 8ft.
To find the GCD, we can use the Euclidean algorithm:
- Divide 13ft by 8ft: 13ft ÷ 8ft = 1 remainder 5ft.
- Divide 8ft by 5ft: 8ft ÷ 5ft = 1 remainder 3ft.
- Divide 5ft by 3ft: 5ft ÷ 3ft = 1 remainder 2ft.
- Divide 3ft by 2ft: 3ft ÷ 2ft = 1 remainder 1ft.
- Divide 2ft by 1ft: 2ft ÷ 1ft = 2 remainder 0ft.
The last nonzero remainder is 1ft, so the GCD of 13ft and 8ft is 1ft.
Step 2: Calculate the area of the cardboard.
The area of the cardboard is given by the product of its length and width:
Area = Length × Width = 13ft × 8ft = 104 square feet.
Step 3: Divide the area by the square of the GCD.
To determine the least number of square pieces, we divide the area of the cardboard by the square of the GCD:
Number of square pieces = Area / (GCD)^2 = 104 square feet / (1ft)^2 = 104.
Therefore, the least number of square pieces into which the given cardboard can be cut is 104.
To find the least number of square pieces into which a cardboard measuring 13 feet long and 8 feet wide can be cut, we need to determine the size of the square piece and then calculate the number of these pieces required to cover the entire area of the cardboard.
Step 1: Find the greatest common divisor (GCD) of the length and width of the cardboard.
The GCD of 13 and 8 is 1.
Step 2: Calculate the area of the cardboard.
The area of the cardboard is given by the product of the length and width:
Area = Length * Width = 13 ft * 8 ft = 104 sq. ft
Step 3: Find the size of the square piece.
To find the size of the square piece, we need to find the largest perfect square that can divide both the length and width evenly. In this case, the GCD is 1, so the largest perfect square is 1.
Step 4: Calculate the number of square pieces required.
To calculate the number of square pieces required, divide the area of the cardboard by the area of the square piece:
Number of square pieces = Area of cardboard / Area of square piece = 104 sq. ft / 1 sq. ft = 104
Therefore, the least number of square pieces into which the cardboard can be cut is 104.