Help PLZ!!!

[penguin520]

A flower garden has the shape ​pictured below. The diameter of the outer circle is
twice the diameter of the inner circle. The
lengths of the walkways are each 6 feet long.
What is the diameter of the inner circle?:cool::cool:

 

[penguin520]

Hey this is mom;
2x=6+6+6+6
2x=24
2x/2=24/2
x=12

 

[jsterkel]

Although your answer is correct, I believe your work is based on an assumption that is not necessarily correct.

If I understand correctly, you are ASSUMING that the radius of the smaller circle is 6 feet. Based on this ASSUMPTION, you can ASSUME that x=12 feet.

In order to prove this, we know that the diameter of the inner circle is "x". We also know the diameter of the outer circle is "twice the diameter " of the inner circle, or 2x.

We can also express the diameter of the outer circle as "x + 6 + 6".

We now have two two different ways to express the diameter of the outer circle. They equal each other, so we can state that
2x = x + 6 + 6
2x = x + 12
2x - x = x + 12 -x
x = 12

This confirms that the diameter of the inner circle is 12 feet.