The length of a rectangular board is 10 centimeters longer than its
width. The width of the board is 26 centimeters. The board is cut
into 9 equal pieces.
a. What is the area of each piece?
b. What are the possible dimensions of each piece?
(Take the dimensions to be whole numbers.)
Board is 26 by (26 + 10) = 36.
Area = 26 * 36 = ?
Divide area by 9, then calculate possible length and width.
26+10=36*26=216+72=936+
104
2345
To find the answers to these questions, we can use the given information about the length and width of the rectangular board. Let's break it down step by step.
Step 1: Determine the length of the rectangular board.
The length of the board is given to be 10 centimeters longer than its width. Since the width is 26 centimeters, we can calculate the length by adding the extra 10 centimeters:
Length = Width + 10
Length = 26 + 10
Length = 36 centimeters
Step 2: Calculate the area of the rectangular board.
The area of a rectangle is given by the formula: Area = Length x Width.
Area = Length x Width
Area = 36 cm x 26 cm
Area = 936 square centimeters
Step 3: Find the area of each piece.
Since the board is cut into 9 equal pieces, we need to divide the total area of the board by 9 to find the area of each piece.
Area of each piece = Total Area of the board / Number of pieces
Area of each piece = 936 square cm / 9
Area of each piece ≈ 104 square centimeters
Therefore, the area of each piece is approximately 104 square centimeters.
Step 4: Determine the possible dimensions of each piece.
To find the possible dimensions of each piece, we need to find pairs of numbers that multiply together to give approximately 104.
Possible pairs of whole numbers whose product is close to 104 are:
1 x 104
2 x 52
4 x 26
8 x 13
Therefore, the possible dimensions of each piece could be:
1 cm x 104 cm
2 cm x 52 cm
4 cm x 26 cm
8 cm x 13 cm
Please note that the dimensions of each piece could vary as long as the product is close to 104 square centimeters and the dimensions are whole numbers.