The length of a rectangular board is 10 cm longer than its width. The width of the board is 26 cm. the board is cut into 9 equal pieces.
What is the area of each piece?
What are the possible dimensions of each piece?
85
the length is clearly 36 cm
The pieces can be (36/9)x26 or 36x(26/9)
Assuming you want integer dimensions, I'd go with the first choice.
Is it 2
To find the area of each piece, we need to calculate the area of the original rectangular board first.
Given that the width of the board is 26 cm, we can determine the length by adding 10 cm to the width:
Length = Width + 10 cm = 26 cm + 10 cm = 36 cm.
To calculate the area, we multiply the length by the width:
Area of the original board = Length × Width = 36 cm × 26 cm = 936 cm².
Since the board is cut into 9 equal pieces, we can divide the total area by the number of pieces to find the area of each piece:
Area of each piece = Area of the original board ÷ Number of pieces = 936 cm² ÷ 9 = 104 cm².
Therefore, the area of each piece is 104 cm².
To determine the possible dimensions of each piece, we can divide the width and length of the original board by the square root of the number of pieces (since the pieces are equal in area).
Width of each piece = Width of the original board ÷ √Number of pieces = 26 cm ÷ √9 = 26 cm ÷ 3 = 8.67 cm (rounded to 2 decimal places).
Length of each piece = Length of the original board ÷ √Number of pieces = 36 cm ÷ √9 = 36 cm ÷ 3 = 12 cm.
Therefore, the possible dimensions of each piece are approximately 8.67 cm by 12 cm (rounded to 2 decimal places).