A triangle has side lengths measuring 3x cm, 7x cm, and h cm. Which expression describes the possible values of h, in cm?

By the triangle inequality, a triangle’s third side must be greater than the difference of the other two sides and less than their sum. Thus |7x − 3x| < h < 7x + 3x, which gives 4x < h < 10x. The endpoints are excluded because they would form a degenerate, flat triangle.

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