The two heights of ABC are 4 and 12 respectively. If the height of the third side is also an integer, then the longest one may be () A. 4B. 5C. 6D. 7

Let the height of the triangle be x, the three sides of the triangle be a, B, c.. 4A = 12C = XB, the solution is a = 3C, B = 12cx, ∵ a-c < B, a + C > b, the solution is 3 < x < 6, ∵ x is an integer, ∵ x can only be 4 or 5, ∵ is an equilateral triangle, ∵ height cannot be 4, ∵ the longest may be 5, so choose B

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