Question

A third ant walks around the perimeter of another rectangle 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.

Answer 1

Let the length and width of the rectangle sheet of paper be $l$ and $w$ respectively. Then the ant walks $l+w+l+w = 2l + 2w = 2(l+w)$ centimeters around the perimeter of the rectangle sheet of paper. Since the ant travels between 18 and 19 centimeters, we have $18 \leq 2(l+w) \leq 19$. Dividing both sides by 2 gives $9 \leq l+w \leq \dfrac{19}{2}$. Since the dimensions of the sheet of paper are given in decimal numbers expressed to the hundredth place, with the tenths and hundredths digits being non-zero, we can only have $l+w = 9.00$ or $l+w = 9.50$.

If $l+w = 9.00$, then $(l,w) = (4.5,4.5)$.

If $l+w = 9.50$, then $(l,w) = (4.75,4.75)$.

Thus, one possibility for the dimensions of the sheet of paper is $\boxed{4.75}$ centimeters by $\boxed{4.75}$ centimeters.