Answer:
The scale factor is 1.5
Step-by-step explanation:
we know that
If two figures are similar, the the ratio of its areas is equal to the scale factor squared and the ratio of its corresponding sides is equal to the scale factor
Let
z-----> the scale factor
x-----> the area of the larger octagon
y----> the area of the smaller octagon
[tex]z^{2} =\frac{x}{y}[/tex]
we have
[tex]x=9\ m^{2}[/tex]
[tex]y=4\ m^{2}[/tex]
substitute
[tex]z^{2} =\frac{9}{4}[/tex]
square root both sides
[tex]z =\frac{3}{2}=1.5[/tex]
therefore
The scale factor of the smaller octagon to the larger octagon is 1.5
