△ABC has integer sides x, y, and z such that xz = 12. How many such triangles are possible?

Question

△ABC has integer sides x, y, and z such that xz = 12. How many such triangles are possible?
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Solution 1

To solve this problem, we need to consider the possible integer pairs (x, z) that multiply to 12. These pairs are (1, 12), (2, 6), (3, 4), (-1, -12), (-2, -6), and (-3, -4). However, since the lengths of the sides of a triangle cannot be negative, we discard the last three pairs.

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