Answer:
The ratio of the areas of the smaller rectangle to the larger rectangle is [tex]\frac{1}{9}[/tex]
Step-by-step explanation:
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
x-----> the area of the smaller rectangle
y----> the area of the larger rectangle
so
[tex]z^{2}=\frac{x}{y}[/tex]
substitute the values
[tex]z^{2}=\frac{20}{180}[/tex]
simplify
[tex]z^{2}=\frac{1}{9}[/tex]
That means, the area of the larger rectangle is 9 times the area of the smaller rectangle
[tex]z=\frac{1}{3}[/tex] ------> the scale factor
That means, the dimensions of the larger rectangle is 3 times the dimensions of the smaller rectangle
