Final answer:
The difference between two consecutive square numbers is represented by the formula 2n + 1, where n is the smaller square's integer root. Therefore, the difference is always an odd number, making options a, b, and c plausible differences for a pair of consecutive squares with d (1 square unit) not fitting the pattern. The correct answer is option D .
Step-by-step explanation:
The difference between two consecutive square numbers can be expressed mathematically. If we consider n to be an integer, then the first square number is n2, and the next consecutive square number is (n+1)2. To find the difference between them, we calculate (n+1)2 - n2, which leads us to 2n + 1. As such, consecutive square numbers differ by an odd number which is 2 times the smaller root plus 1. For instance, the difference between 32 (9) and 42 (16) is 16 - 9 = 7, which is 2 times 3 plus 1.
Looking at the given options, only (d) 1 square unit seems out of place because the difference between two consecutive square numbers is always an odd number as it is given by the formula 2n + 1, where n is an integer, and the other options (a), (b), and (c) are odd numbers, fitting the pattern for the difference between consecutive squares (18 squares, 17 squares, and 35 squares).
Some of the unconnected information regarding perimeters, displacements, cross-sectional areas, and other mathematical topics seems to be added as an SEO attempt but doesn't apply to the initial question about the difference between consecutive square numbers.