Answer :
Answer:
The radius of the circle A is [tex]\sqrt{2}[/tex] times greater than the radius of circle B
Step-by-step explanation:
step 1
Find the scale factor
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 clock A
y----> the area of the clock B
[tex]z^{2}=\frac{x}{y}[/tex] -----> equation A
we have
[tex]x=2y[/tex] -----> equation B
substitute equation B in equation A
[tex]z^{2}=\frac{2y}{y}=2[/tex]
square root both sides
[tex]z=\sqrt{2}[/tex]
step 2
Find how many times greater is the radius of Clock A than the Clock B radius
we know that
If two figures are similar, then the ratio of its corresponding sides is equal to the scale factor
Let
z-----> the scale factor
x----> the radius of the clock A
y----> the radius of the clock B
[tex]z=\frac{x}{y}[/tex]
we have
[tex]z=\sqrt{2}[/tex]
substitute
[tex]\sqrt{2}=\frac{x}{y}[/tex]
[tex]x=\sqrt{2}y[/tex]
therefore
The radius of the circle A is [tex]\sqrt{2}[/tex] times greater than the radius of circle B