Which set of numbers can represent the side lengths, in inches, of an acute triangle?

For a triangle with side lengths a ≤ b ≤ c to be acute, it must satisfy a² + b² > c². For 5, 7, and 8, the triangle inequality holds, and 5² + 7² = 74 > 8² = 64, so the triangle is acute. The other choices either fail this test or are obtuse: for 4, 5, 7, 4² + 5² < 7², and for 6, 7, 10 and 7, 9, 12 the sums of the two shorter squares are also less than the longest side’s square.

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