The side-lengths a, b and c of a right triangle are integers

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Since k>0, we have c > b > a.
Case 1: b = 56
Since c = k + 56, a = 56 – k and c^2 = a^2 + 56, we have c = 70.
Case 2: a = 56
Since 2b = c + 56 and c^2 = 56^2 + b^2,
c = 2b – 56.
Plugging this into c^2 = 56^2 + b^2 yields
(2b – 56)^2 = 56^2 + b^2
and we solve this equation to give
4b^2 – 224 b + 56^2 = 56^2 + b^2
3b^2 – 224 b = 0
b(3b – 224) =0
b = 224/3 since b is positive.
So,
c =2b – 56 = 448/3 – 56 = 280/3, which is not an integer.
Thus, the length of the largest side is 70.
Therefore, the answer is C.
Answer: C