Answer:
Part 1) The ratio of the perimeters of the larger figure to the smaller figure is equal to [tex]\frac{16}{13}[/tex]
Part 2) The ratio of the areas of the larger figure to the smaller figure is [tex]\frac{256}{169}[/tex]
Step-by-step explanation:
Part 1) What is the ratio of the perimeters of the larger figure to the smaller figure?
we know that
If two figures are similar, then the ratio of its corresponding sides is proportional, and this ratio is called the scale factor
Let
z-----> the scale factor
In this problem
The scale factor is equal to
[tex]z=\frac{32}{26}[/tex]
Simplify
[tex]z=\frac{16}{13}[/tex]
Remember
If two figures are similar, then the ratio of its perimeters is equal to the scale factor
so
The ratio of the perimeters of the larger figure to the smaller figure is equal to [tex]\frac{16}{13}[/tex]
Part 2) What is the ratio of the areas of the larger figure to the smaller figure?
we know that
If two figures are similar, then the ratio of its areas is equal to the scale factor squared
Let
z-----> the scale factor
we have
[tex]z=\frac{16}{13}[/tex]
so
[tex]z^{2}=(\frac{16}{13})^{2}=\frac{256}{169}[/tex]
therefore
The ratio of the areas of the larger figure to the smaller figure is [tex]\frac{256}{169}[/tex]
