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. im confused and i need help
Let's assume the length of the paper is $L$ and the width is $W$.
Since the ant walks around the perimeter of the paper, the distance it travels is equal to the sum of all four sides of the paper.
We can express this distance as $2L + 2W$.
We are told that this distance is between 18 and 19 centimeters, so we can write the inequality:
$18 < 2L + 2W < 19$
Dividing both sides of the inequality by $2$, we get:
$9 < L + W < \frac{19}{2}$
Since the dimensions are given in decimal numbers expressed to the hundredth place, with the tenths and hundredths digits being non-zero, we can assume that $L$ and $W$ are slightly less than $\frac{19}{2}$.
For example, let's assume $L = 9.45$ and $W = 0.55$.
The sum of the two dimensions is $L + W = 10$ which is between $9$ and $\frac{19}{2}$.
Hence, one possibility for the dimensions of the sheet of paper is $9.45$ cm by $0.55$ cm.
To find the dimensions of the sheet of paper, we can use the fact that the ant walks around the perimeter of the rectangle.
Let's assume the dimensions of the rectangle are length (L) and width (W).
The perimeter of a rectangle is given by the formula: P = 2L + 2W.
We know that the ant walks between 18 and 19 centimeters, so we can write the inequality as:
18 ≤ 2L + 2W ≤ 19.
Simplifying the inequality, we get:
9 ≤ L + W ≤ 9.5.
Since the dimensions of the rectangle are given in decimal numbers expressed to the hundredth place, and the tenths and hundredths digits are non-zero, we can determine one possible set of dimensions for the rectangle by looking for values of L and W that satisfy the inequality.
Let's choose L = 5 and W = 4, which satisfies the inequality:
9 ≤ 5 + 4 ≤ 9.5.
Therefore, one possible set of dimensions for the sheet of paper is 5 centimeters by 4 centimeters.