Answer:
C 4 cm, 6 cm, 10 cm
Step-by-step explanation:
You should recognize that the lengths 6, 8, 10 have the ratio 3 : 4 : 5, the ratios of sides in the smallest Pythagorean triple. Since 6 and 10 are two of these numbers, with 10 being the largest, the only possible third side is 8. There is no such thing as a 4, 6, 10 right triangle.
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You can check whether each triple satisfies the Pythagorean theorem:
A 6² +8² = 10² ⇒ 36 +64 = 100 . . . true
B 12² +35² = 37² ⇒ 144 +1225 = 1369 . . . true
C 4² +6² = 10² ⇒ 16 +36 = 100 . . . FALSE
D 10² +24² = 26² ⇒ 100 +576 = 676 . . . true
