Question

Two clocks are circular. Clock A has twice the area Clock B. How many times greater is the radius of Clock A than the Clock B radius?

Answer 1

Answer:

The radius of the circle A is $\sqrt{2}$ 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

$z^{2}=\frac{x}{y}$ -----> equation A

we have

$x=2y$ -----> equation B

substitute equation B in equation A

$z^{2}=\frac{2y}{y}=2$

square root both sides

$z=\sqrt{2}$

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

$z=\frac{x}{y}$

we have

$z=\sqrt{2}$

substitute

$\sqrt{2}=\frac{x}{y}$

$x=\sqrt{2}y$

therefore

The radius of the circle A is $\sqrt{2}$ times greater than the radius of circle B