Answer:
The ratio of their corresponding side lengths is equal to [tex]\frac{1}{3}[/tex]
Step-by-step explanation:
step 1
Find the scale factor
we know that
If two figures are similar, then the ratio of its surface areas is equal to the scale factor squared
Let
z-------> the scale factor
x----> the area of the smaller solid
y----> the area of the larger solid
so
[tex]z^{2}=\frac{x}{y}[/tex]
In this problem we have
[tex]\frac{x}{y} =\frac{16}{144}[/tex]
substitute
[tex]z^{2}=\frac{16}{144}[/tex]
square root both sides
[tex]z=\frac{4}{12}[/tex] ------> scale factor
Simplify
[tex]z=\frac{1}{3}[/tex]
step 2
Find the ratio of their corresponding side lengths
we know that
If two figures are similar, then the ratio of its corresponding sides is equal to the scale factor
In this problem we have that the scale factor is equal to [tex]\frac{1}{3}[/tex]
therefore
The ratio of their corresponding side lengths is equal to [tex]\frac{1}{3}[/tex]
