VeritasKarishma plz explain

I often propose the concept of "trying to construct the figure" in Geometry DS questions. They tell you whether the statements are sufficient or not.

(1) Angle ABC is 90 degrees.

If angle is 90 degrees, we know that we can use the pythagorean theorem to get the third side.
Sufficient alone.

(2) The area of the triangle is 30.

Say base is 13 and we move the side of length 5. The angle made by these two sides can go from 0 degrees to 180 degrees (exclusive) to make a triangle. The maximum area will be obtained when the angle is 90 degrees because the altitude in that case is 5, same as the length of the side.

When the angle is less than 90 degrees, there will be a point when the area will be 30 and the third side will have a certain length at that point. Here, altitude will be 60/13.

But when the angle is more than 90 degrees (obtuse angle), again there will be a point when the area is 30. The side lengths in the two cases will be different.



Answer (A)
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