Tell whether the pair of polygons is similar or not. Explain why or why not 1 is 14 feet by 9 feet and the second is 5.1 feet by 2.3 feet.
To determine whether two polygons are similar, their corresponding sides need to have the same ratio, and their corresponding angles need to be equal. Similar polygons are essentially enlargements or reductions of one another.
For the rectangles provided, let's consider the ratios of the corresponding sides:
First rectangle: 14 feet by 9 feet
Second rectangle: 5.1 feet by 2.3 feet
Now we compute the ratios of the lengths to the widths for both rectangles:
For the first rectangle:
Ratio = length / width = 14 feet / 9 feet ≈ 1.5556 (rounded to four decimal places)
For the second rectangle:
Ratio = length / width = 5.1 feet / 2.3 feet ≈ 2.2174 (rounded to four decimal places)
Since the ratios of the corresponding sides (length to width) are not equal, the two rectangles are not similar. For two rectangles to be similar, their corresponding side lengths must have the same ratio, which indicates that they have the same shape with proportionally scaled sizes. Because these two rectangles have different shape ratios, they are not similar.