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The squares of three consecutive positive integers add up to 245. What is the sum of the three integers?

Competition practiceAlgebra

A27
B24
C30
D81

Step-by-Step Solution

Let the middle one be

m : (m - 1)^{2} + m^{2} + (m + 1)^{2} = 3 m^{2} + 2 = 245

, so

m^{2} = 81

and

m = 9

. The integers 8, 9, 10 add up to 27.

Answer: A) 27

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