A third ant walks around the perimeter of another rectangular sheet of paper. The dimensions of this sheet of paper are given in decimal numbers expressed to the hundredth place, with the tenths and hundredths digits being non-zero. If the ant travels between 18 and 19 centimeters, what are the dimensions of the sheet of paper? Give one possibility.
Let the length and width of the rectangular sheet of paper be $l$ and $w$ centimeters, respectively. The perimeter of the paper is $2(l+w)$. Since the ant walks around the perimeter exactly three times, the distance it travels is $3 \cdot 2(l+w) = 6(l+w)$ centimeters.
Since the distance is between 18 and 19 centimeters, we have $18 \le 6(l+w) \le 19$. Dividing by 6, we get $3 \le l+w \le \frac{19}{6}$.
Now we need to find a pair of positive decimal numbers $l$ and $w$ that satisfy $3 \le l+w \le \frac{19}{6}$. Let's try taking $l = 1.5$ and $w = 1.5$. Then $l+w = 3$, which satisfies the inequality. Therefore, one possibility for the dimensions of the sheet of paper is $\boxed{1.5 \times 1.5}$.
what??
I apologize for my previous incorrect response. Let's approach the problem again.
Let the length and width of the rectangular sheet of paper be $l$ and $w$ centimeters, respectively. The ant walks around the perimeter once, which is $2(l+w)$ centimeters. Since the ant walks around the perimeter exactly three times, the distance it travels is $3 \cdot 2(l+w) = 6(l+w)$ centimeters.
The problem states that the distance traveled by the ant is between 18 and 19 centimeters. Therefore, we have $18 \le 6(l+w) \le 19$. Dividing by 6, we get $3 \le l+w \le \frac{19}{6}$.
We want to find positive decimal numbers $l$ and $w$ such that $l+w$ is between 3 and $\frac{19}{6}$. One possible solution is when $l = 1.4$ and $w = 1.6$. In this case, $l+w = 1.4 + 1.6 = 3$, which is between 3 and $\frac{19}{6}$.
Therefore, one possibility for the dimensions of the sheet of paper is $\boxed{1.4 \times 1.6}$.
can you show the answer without the $ signs
Certainly! One possibility for the dimensions of the sheet of paper is 1.4 centimeters by 1.6 centimeters.
Let's assume the dimensions of the rectangular sheet of paper are length (L) and width (W) in centimeters.
When the ant walks around the perimeter of the sheet of paper, it covers a distance equal to twice the length plus twice the width of the paper.
So, the possible dimensions of the sheet of paper can be given by the equation:
2L + 2W = between 18 and 19 centimeters
Since the dimensions are given in decimal numbers expressed to the hundredth place, we can express one possibility as follows:
Let's assume L = 8.99 cm and W = 0.01 cm
Now, let's calculate the distance covered when the ant walks around the perimeter:
2L + 2W = 2(8.99) + 2(0.01) = 17.98 + 0.02 = 17.98 + 0.02 = 17.99 cm
So, one possibility for the dimensions of the rectangular sheet of paper is 8.99 cm by 0.01 cm.
To determine the dimensions of the rectangular sheet of paper, we can use the perimeter formula for a rectangle. Let's assume that the length of the rectangle is L and the width is W.
The perimeter of a rectangle is given by the formula: P = 2L + 2W
Now, we know that the ant travels between 18 and 19 centimeters. The ant walks around the perimeter of the rectangle, so we have the following inequality: 18 < P < 19.
Substituting the perimeter formula into the inequality, we get: 18 < 2L + 2W < 19.
Since the length and width of the rectangle are in decimal numbers expressed to the hundredth place, we can assume that both L and W are decimal numbers with the tenths and hundredths digits being non-zero.
To find one possibility for the dimensions of the sheet of paper, we need to find a combination of L and W that satisfies the inequality. Let's try different combinations until we find a solution.
Here's one possibility:
Let L = 9.00 centimeters and W = 0.50 centimeters.
Substituting these values into the perimeter formula, we get: P = 2(9.00) + 2(0.50) = 19.00 centimeters.
Since 18 < 19 < 19, this combination satisfies the given conditions.
Therefore, one possibility for the dimensions of the rectangular sheet of paper is 9.00 centimeters by 0.50 centimeters.