Question

The dimensions of a rectangle of area 72 are whole numbers. List the dimensions of all such rectangles. If two of these rectangles are chosen at random, what is the probability that each has a perimeter greater than 40?

Answer 1

The dimensions of all rectangles with an area of 72 are listed as (1, 72), (2, 36), (3, 24), (4, 18), (6, 12), and (8, 9). To find the probability of randomly choosing two rectangles with a perimeter greater than 40, we need to calculate the total number of rectangles and the number of rectangles with a perimeter greater than 40. These values can be used to calculate the probability.

Step-by-step explanation:

To find the dimensions of a rectangle with an area of 72, we can list all possible whole number pairs whose product is 72. These pairs are: (1, 72), (2, 36), (3, 24), (4, 18), (6, 12), and (8, 9). To find the probability that each randomly chosen rectangle has a perimeter greater than 40, we need to determine the total number of rectangles, as well as the number of rectangles with a perimeter greater than 40. The probability can then be calculated by dividing the number of rectangles with a perimeter greater than 40 by the total number of rectangles.