Suppose that each dimension of the sheet of paper described in question 1 is increased by one inch. How many inches will the ant travel in this case? Explain your thinking.
In question 1, we found that the ant would travel a total distance of 56 inches if it were to walk along the perimeter of the original sheet of paper.
If each dimension of the sheet of paper is increased by one inch, it means that each side of the sheet of paper is now extended on both ends by one inch. Therefore, the length and width of the sheet of paper have now increased by two inches each.
When the length and width of the sheet of paper increase by two inches, the ant will now have to walk along a longer perimeter. To find the new perimeter, we add two inches to both the length and width, and then multiply each by 2 to account for all four sides.
Let's say the original length and width of the sheet of paper are x inches.
After adding two inches to each side, the new length and width would be (x + 2) inches.
The new perimeter would be:
Perimeter = 2(length + width) = 2((x + 2) + (x + 2)) = 2(2x + 4) = 4x + 8
So now, the ant would have to travel a distance of (4x + 8) inches.
Since we don't have the exact measurements of the original sheet of paper, we can't calculate the exact answer in this case. However, what we do know is that the ant will have to travel a longer distance compared to the original sheet of paper.
i thought the answer to question 1 was thirteen
In order to calculate the distance the ant will travel when each dimension of the sheet of paper is increased by one inch, we need to consider the perimeter of the paper.
Let's assume the original dimensions of the sheet of paper in Question 1 were length 'L' and width 'W'. The perimeter of the original paper can be calculated using the formula: Perimeter = 2(L + W).
When each dimension is increased by one inch, the new length becomes 'L + 1' and the new width becomes 'W + 1'. Therefore, the new perimeter can be calculated as: New Perimeter = 2((L + 1) + (W + 1)).
Expanding the equation gives us: New Perimeter = 2(L + W + 1 + 1) = 2(L + W + 2).
To find the increase in distance traveled by the ant, we subtract the original perimeter from the new perimeter:
Increased distance traveled = New Perimeter - Perimeter
= (2(L + W + 2)) - (2(L + W))
= 2L + 2W + 4 - 2L - 2W
= 4.
Therefore, the ant will travel an additional 4 inches when each dimension of the sheet of paper is increased by one inch.
To determine how many inches the ant will travel when each dimension of the sheet of paper described in question 1 is increased by one inch, we need to consider the perimeter of the new paper size.
In question 1, let's assume the length of the paper is L inches and the width is W inches. The perimeter of the sheet is given by the formula:
Perimeter = 2L + 2W
Now, when both dimensions are increased by one inch, the new length will be (L + 1) inches and the new width will be (W + 1) inches.
So, the new perimeter can be calculated as:
New Perimeter = 2(L + 1) + 2(W + 1)
= 2L + 2 + 2W + 2
= (2L + 2W) + (2 + 2)
= 2L + 2W + 4
Compared to the original perimeter, the increase in inches can be found by subtracting the original perimeter from the new perimeter:
Increase = New Perimeter - Perimeter
= (2L + 2W + 4) - (2L + 2W)
= 4
Hence, we can conclude that the ant will travel an additional 4 inches when each dimension of the sheet of paper is increased by one inch.