Answer: 220 meters
Step-by-step explanation:
Let’s denote the radius of the outer circle as R and the radius of the inner circle as r. The outer circumference is given by 2πR, and the inner circumference is 2πr.
We have the following ratio:
[ \frac{{\text{{Outer Circumference}}}}{{\text{{Inner Circumference}}}} = \frac{{2πR}}{{2πr}} = \frac{{2}}{{22}} ]
Solving for R and r:
[ \frac{{R}}{{r}} = \frac{{23}}{{22}} ]
Let’s express R and r in terms of x:
[ R = 23x ] [ r = 22x ]
Now, we know that the width of the path is 5 meters:
[ R - r = 5 ] [ 23x - 22x = 5 ] [ x = 5 ]
Therefore, the radius of the inner circle is:
[ r = 22x = 22 \times 5 = 110 , \text{meters} ]
The diameter of the inner circle is twice the radius:
[ \text{Diameter of inner circle} = 2r = 2 \times 110 = 220 , \text{meters} ]
Hence, the diameter of the inner circle is 220 meters
