9514 1404 393
Answer:
(c) 9, 24, 26
Explanation:
If you're familiar with Pythagorean triples, you may recognize that 10-24-26 is a doubling of the common 5-12-13 triple seen in many problems. That means the triple 9-24-26 cannot be a right triangle.
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The "form factor" of f = a^2 +b^2 -c^2, where c is the longest side length, can signal the kind of triangle it is. f=0 indicates a right triangle (values satisfy the Pythagorean theorem). When there are a lot of numbers to try, I like to let a calculator or spreadsheet do the math. (See attached).
As indicated above, the 9-24-26 triple cannot be a right triangle. For f < 0, it will be an obtuse triangle.