<p>It has to be a right triangle because the question asks for the "greatest possible area of a triangle." A right triangle being the largest area is just one of those known shortcuts one can rely on. Something of the same nature might appear on tests such as the GMAT or GRE, but with squares. It is, however, NOT needed to know this to solve the problem. If you do, that is great, if not, it's no biggie!</p>

<p>In the simplest terms, just think that a right triangle does maximize the possible values of the **base and the height**. You can play around with some sketches of possible triangles and it will make sense. Remember the basic rules for the sizes of the sides. </p>

<p>Another alternative is to check your basic trig for the area of a triangle and the maximum values of sin, but that goes beyond the SAT.</p>