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Answer:
15 centimeters.
Step-by-step explanation:
If the ratio of two sides of similar octagons is 5:7, then the larger octagon has a side length that is 7/5 times the smaller one. If the measure of the side of the larger octagon is 21, then the measure of the smaller one is 5/7 times that, which is 5/7 * 21 = 15 centimeters.