The sides of a triangle have lengths of x, x + 4, and 20. If the longest side is 20, which of the following values of x would make the triangle acute?

For a triangle with longest side 20, it is acute when the sum of the squares of the other two sides is greater than 20² = 400. At x = 14, the other sides are 14 and 18, and 14² + 18² = 196 + 324 = 520, which is greater than 400. Therefore, x = 14, choice D, makes the triangle acute.

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