OG. Q332. Page 282

[JackH825]

Geometry.
Does the second statement not tell us that the triangle is an isosceles triangle? Therefore, we can find out the lengths by knowing that the third side is 2√x. I appreciate that both statements together show that it is an equilateral triangle.

[Sage Pearce-Higgins]

This is about DS332 from OG2020. Yes, the second statement tells us that the triangle is an isosceles triangle. However, that doesn't mean that we can calculate the length of side QT. Think that an isosceles triangle with one side length 6 can have multiple possibilities for the lengths of the two equal sides. It's perhaps clearer to turn the triangle around so that the 6 is the base and consider that it could be a thin, flat triangle with the equal sides a little longer than 3, or it could be a tall, pointy triangle with much longer side lengths. These variants will affect the area of the triangle, meaning that we'd get multiple possible answers to the question in this DS problem, hence statement 2 is insufficient.