Final answer:
Using proportions with a given scale factor allows us to determine the actual lengths and widths from scaled dimensions of a rectangle, and it is possible for a rectangle to have a length to width ratio of 4:7.
Step-by-step explanation:
The question asks us to determine if it is possible for a rectangle to have the ratio of its length to its width as 4:7. We can verify this ratio by using proportions. For example, assuming we are given a scale factor, we can compare the scaled dimensions to the actual dimensions. For instance, if we have a scale factor of 1:10, and a scaled length of 14 units, then the proportion for length would be Length-scale/actual = 14/1 = 1/10. Similarly, if we know the scaled width, we could set up a proportion for width using the same scale factor. If the scale dimension is 4, and we are looking to find the actual dimension using the scale factor 1:4, we can set up a proportion as follows: 1:2 = 4:x, where x represents the unknown actual dimension.
In relation to the provided information, if a scaled length is given, and the actual length is unknown, one can form a proportion such as Length-scale/actual = 8/w. By solving this proportion, we can find the actual length of a rectangle when its scale length is known. For width, the proportion would be Width-scale/actual = 4/1, which can also be solved to find the actual width. These examples illustrate how we use scale factors and proportions to determine actual lengths and widths from scaled dimensions.
Lastly, the statement regarding the application of the Pythagorean theorem is True. The Pythagorean theorem can indeed be used to calculate the length of the resultant vector when two vectors at right angles to each other are added.