Final answer:
The ratio of the circumferences of the two circles is 8:7.
Step-by-step explanation:
To find the ratio of the circumferences, we need to find the radius of each circle. Let's assume the radius of the first circle is r1 and the radius of the second circle is r2. Since the areas of the circles are in the ratio 49:64, we can set up the following equation:
49/r1² = 64/r2²
Cross multiplying, we get 49r2² = 64r1². Taking the square root of both sides, we get r2/r1 = √(64/49) = 8/7.
Therefore, the ratio of the circumferences is 2πr2/2πr1 = r2/r1 = 8/7.