Question

4. 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.

Answer 1

Let's assume one dimension of the rectangular sheet of paper is x centimeters and the other dimension is y centimeters.

When the ant walks around the perimeter of the rectangular sheet of paper, it covers a distance equal to 2x + 2y centimeters.

We are given that the ant travels between 18 and 19 centimeters, so we can write the inequality as follows:

18 < 2x + 2y < 19

Dividing the entire inequality by 2, we get:

9 < x + y < 9.5

Since x and y are decimal numbers expressed to the hundredth place, we need to find two numbers whose sum is between 9 and 9.5.

One possibility is x = 4.50 and y = 4.50. In this case, x + y = 4.50 + 4.50 = 9, which is between 9 and 9.5.

So, one possibility for the dimensions of the sheet of paper is 4.50 cm by 4.50 cm.