In triangle ABC, side AB is 5 inches. . .

[Vincen]

In triangle ABC, side AB is 5 inches and side BC is 7 inches. What is the area of the triangle ABC?

(1) Angle ABC is 90 degrees
(2) Triangle ABC is a right triangle

The OA is A.

Why the statement (2) is not sufficient too? Both statements says almos the same. What is the difference?

[ErikaPrepScholar]

The trap in this question is that the test makers want you to think that the two statements say the same thing. But they actually don't!

Statement 1 tells us that Angle ABC is 90 degrees. This means that AB and BC are the base and height of the triangle and that AC is the hypothenuse. So to get the area, we use A = (1/2)bh = 1/2(5)(7). SUFFICIENT.

Statement 2 tells us that Triangle ABC has a 90 degree angle. However, it doesn't tell us which angle is 90 degrees: it could be ABC, ACB, or BAC. This means that we don't know if AB and BC are the base and height of the triangle. They might be! But AB could be the base and BC could be the hypotenuse. This would mean that the height of the triangle would *not* be 7, which would then change the area of the triangle. INSUFFICIENT.