riangle ABC has integer sides x, y, z such that xz = 12. How many such triangles are possible?Choices:- 8 6 9 12Save AnswerSkip this questionFinish Exam

The problem states that the sides of the triangle are integers and that the product of two sides, x and z, is 12.

The pairs of integers that multiply to 12 are (1,12), (2,6), (3,4), (-1,-12), (-2,-6), (-3,-4), (12,1), (6,2), (4,3), (-12,-1), (-6,-2), and (-4,-3).

However, in a triangle, the length of one side must be less than the sum of the lengths of the other two sides. This is known as the triangle inequality theorem.

So, we can eliminate the pairs (1,12), (-1,-12), (12,1), and (-12,-1) because in these cases, one side (12) is equal to the sum of the other two sides (1 and 11 or -1 and -11), which violates the triangle inequality theorem.

This leaves us with the pairs (2,6), (3,4), (-2,-6), (-3,-4), (6,2), (4,3), (-6,-2), and (-4,-3).

So, there are 8 possible triangles.

Therefore, the answer is 8.