In Triangle ABC, if AB = x, BC = y, and AC = x + y
, which of the three angles of Triangle ABC has the least degree measure?
(1) x = y + 1
(2) y = 4
I think there is a typo in this question.
We know that a rule in triangles theory is:
|Side 2 - Side 3| < Side 1 < Side 2 + Side 3
So, how can AC (x+y) be equal to AB (x) and BC (y)?
You are right, the question is flawed. They just took and incorrectly rephrased question from OG, which is:
The shortest side is always opposite the smallest angle.
The longest side is always opposite the largest angle.
The length of any side of a triangle must be larger than the positive difference of the other two sides, but smaller than the sum of the other two sides.
(1) y = x + 3 --> PR is the longest side, hence opposite the largest angle PQR. Sufficient.
(2) x = 2 --> PQ=2 and QR=4 --> 2<PR<6. So, we cannot determine which side is the longest QR or PR. Not sufficient.