Doubt - When it says Triangle ABC - doesn't it mean the way it is written angle B is right angled?

OFFICIAL EXPLANATION


37. Angle $A C B$ equals $90^{\circ}$ and $A B=\mathbf{1 7}$ only. If angle $A C B=90^{\circ}$, then 8 and 15 are the base and height, and you can calculate the area. The first statement is sufficient.

If $A B=17$, you can plug 8,15 , and 17 into the Pythagorean theorem to see whether you get a true statement. Use 17 as the hypotenuse in the Pythagorean theorem because 17 is the longest side:

$$\(\begin{aligned} & 8^2+15^2=17^2 \\ & 64+225=289 \\ & 289=289 \end{aligned}\)$$


Since this is true, the triangle is a right triangle with the right angle at $C$. If angle $$A C B=90^{\circ}$$, then 8 and 15 are the base and height, and you can calculate the area. (Since 8-15-17 is a Pythagorean triple, if you had that fact memorized, you could skip the step above.) The second statement is sufficient.

Knowing that $$A B C$$ is a right triangle (the third statement) is not sufficient to calculate the area because it's not specified which angle is the right angle. A triangle with sides of 8 and 15 could have hypotenuse 17 , but another scenario is possible: perhaps 15 is the hypotenuse. In this case, the third side is shorter than 15 , and the area is smaller than in the $8-15-17$ scenario.

I do not see such assumption reading the question.

The question is asking you a specfic thing : the area and IF the information provided are sufficient on its own.

This is kinda like a DS on the GMAT