Answer : The figure of the new rectangle is shown below.
Step-by-step explanation :
As we are given that:
Length of rectangle = 9 inches
Width of rectangle = 12 inches
When the rectangle is dilated by a scale factor of 3.5 then it create a new rectangle.
Now we have to determine the figure of the new rectangle.
Formula of scale factor is:
![\text{Scale factor}=\frac{\text{Larger length}}{\text{Smaller length}}](https://tex.z-dn.net/?f=%5Ctext%7BScale%20factor%7D%3D%5Cfrac%7B%5Ctext%7BLarger%20length%7D%7D%7B%5Ctext%7BSmaller%20length%7D%7D)
Given:
Scale factor = 3.5
The length of new rectangle will be:
![\text{Scale factor}=\frac{\text{Larger length}}{\text{Smaller length}}](https://tex.z-dn.net/?f=%5Ctext%7BScale%20factor%7D%3D%5Cfrac%7B%5Ctext%7BLarger%20length%7D%7D%7B%5Ctext%7BSmaller%20length%7D%7D)
![3.5=\frac{\text{Larger length}}{9}](https://tex.z-dn.net/?f=3.5%3D%5Cfrac%7B%5Ctext%7BLarger%20length%7D%7D%7B9%7D)
![\text{Larger length}=3.5\times 9](https://tex.z-dn.net/?f=%5Ctext%7BLarger%20length%7D%3D3.5%5Ctimes%209)
inches
and,
The width of new rectangle will be:
![\text{Scale factor}=\frac{\text{Larger width}}{\text{Smaller width}}](https://tex.z-dn.net/?f=%5Ctext%7BScale%20factor%7D%3D%5Cfrac%7B%5Ctext%7BLarger%20width%7D%7D%7B%5Ctext%7BSmaller%20width%7D%7D)
![3.5=\frac{\text{Larger width}}{12}](https://tex.z-dn.net/?f=3.5%3D%5Cfrac%7B%5Ctext%7BLarger%20width%7D%7D%7B12%7D)
![\text{Larger width}=3.5\times 12](https://tex.z-dn.net/?f=%5Ctext%7BLarger%20width%7D%3D3.5%5Ctimes%2012)
inches
Thus, the figure of the new rectangle is shown below.