Guessing the third side of the triangle from the given two sides

Question

My solution:-

We know that the length of the third side of a triangle is between the sum of the two sides and the difference between the two sides.

So according to the question the third side $x$, should follow this condition, $29>x>7$. So a probable value of $x$ is 28. So the answer should be II only. But this option is non-existent.

So is the question above or more specifically the options for the questions formulated wrongly?

If there's any problem in my question please let me know. Thanks!

Answer 1

The problem doesn't say that Q, R, and S are the vertices of a (non-degenerate) triangle, only that they are points on the plane. They may all be on the same line. Therefore, you want $7\le x\le 29$, and (D) is the correct answer.

Answer 2

They never said that $PQR$ was a triangle. If you allow all three points to be collinear, then $7$ and $29$ are also possible.