Answer:
Option A is correct
The ratio of a pair of corresponding sides is 1/4
Step-by-step explanation:
Definition:
If two polygons are similar, then
the area of similar figure is the square of the ratio of its corresponding sides.
As per the statement:
Two similar polygons have areas of 4 square inches and 64 square inches
Let the corresponding sides of the polynomials are a and b.
then by definition we have;
[tex]\frac{4}{64}=\frac{a^2}{b^2}[/tex]
⇒[tex]\frac{1}{16} = (\frac{a}{b})^2[/tex]
⇒[tex]\sqrt{\frac{1}{16}} =\frac{a}{b}[/tex]
⇒[tex]\frac{1}{4} = \frac{a}{b}[/tex]
or
[tex]\frac{a}{b} = \frac{1}{4}[/tex]
Therefore, The ratio of a pair of corresponding sides is 1/4.
