blueseas wrote:
If AB=3, what is the shortest side of triangle ABC?
(1) AC=5
(2) The perimeter of ΔABC is 13.
From F.S 1, we get a valid triangle for AC=5 and BC=4, and the smallest side is AB.
Again, for BC=2.1, we get another valid triangle and this time, the smallest side is BC. As we get 2 different answers, Insufficient.
From F.S 2, we know that
AC+BC = 13-3 =
10. Now, we know that the difference of 2 sides must be less than the third side of a valid triangle.
Thus, as have |AC-BC|<3. Replacing the value of AC, we get \(|10-BC-BC|<3 \to -3<10-2BC<3 \to 3.5<BC<6.5\). Similarly, we will get the same range for AC. Thus, as both of them are greater than 3.5, the least value WILL BE for the side AB=3. Sufficient.
B.