Final answer:
A circle is different from a square, triangle, and rectangle as it is defined by a single measure (radius or diameter), and does not have separate height and width. In comparing areas, the area of a square scales with the square of the scale factor, so a larger square with double the side length will have an area four times larger.
Step-by-step explanation:
When asked to identify the shape that is different by using ratios of height and width, we can analyze a circle, square, triangle, and rectangle. A circle does not have height and width in the same sense as the other shapes; it is defined by a single measure: its radius or diameter. A square has equal sides, and its ratio of height to width is always 1:1. A triangle can be of various types, but its height to width ratio changes based on the type, and it does not necessarily have a straightforward height to width correspondence. A rectangle is defined by its length and its width and depending on proportions, this ratio can vary, but it is unlike a square because its sides are not all equal.
However, in the context of finding the shape that is different based on the concept of area, we acknowledge that comparing areas of shapes involves different formulas. For example, the area of a square is found by squaring its side length, which aligns with the rule that the ratio of areas of similar figures is the square of the scale factor. If two squares have a scale factor of 2, then the area of the larger square is 4 times larger than that of the smaller square.