In the Courses>Quantitative Section>Data Sufficiency, the following example is posted :-
Example 1. Triangle ABC has one angle equal to 90 degrees and AB equal to 5 inches, what is the area of ABC?
(1) BC = 4
(2) AC = 12
The issue that is subsequently discussed is whether each statement is sufficient to answer the question and about the possibility of 3-4-5 or 5-12-13 triangles i.e a different solution per statement both right in themselves, but both don't talk simultaneously about the same triangle.
My question is : Aren't we making an unwarranted assumption based on "nice numbers" combinations ?
We directly consider AB=5 as the hypotenuse and then assume that BC=4 is one of the non-hypotenuse sides and arrive at the convenient conclusion that it must be a 3-4-5 triangle. What if AB=5 given is one of the non-hypotenuse sides and BC=4 is another non hypotenuse side ?
And similarly for the other triangle - it could be 5-12-13 but it also could be 5-10.909-12. So in this case the answer would have to be an E right ?
I think I may be missing something major otherwise it just doesn's seem to make sense to me....