If the three sides of the triangle ABC are a, B, C and satisfy the following conditions: A2 + B2 + C2 + 338 = 10A + 24B + 26c, then the height of the longest side of the triangle ABC is () A. 8B. 125C. 6013D. 245

∵ A2 + B2 + C2 + 338 = 10A + 24B + 26c, ∵ A2 + B2 + C2 + 338-10a-24b-26c = 0, ∵ a2-10a + 25 + b2-24b + 144 + c2-26c + 169 = 0, ∵ a-5) 2 + (B-12) 2 + (C-13) 2 = 0, ∵ a = 5, B = 12, C = 13. ∵ A2 + B2 = C2. ∵ triangle ABC is a right triangle

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