This question asks about solving for the area of a right triangle. We'll need to know that the area of a triangle is
A = (1/2)bh. This means that if we know that base and the height of the triangle, we can solve for the area. Let's look at each statement individually.
Statement 1
This statement tells us the length of two sides of the triangle: AB and BC. However, it doesn't tell us what the relationship between the two sides is - are they the base and the height? The base and the hypotenuse? The height and the hypotenuse? So the triangle might look like this:
Or it might look like this:
The two triangles will have different bases and, thus, different areas.
Statement 1 is insufficient.
Statement 2
This statement tells us that angle ABC is 90 degrees. This tells us nothing about the lengths of the sides: the triangle could be really, really small or really, really big.
Statement 2 is insufficient.
BOTH
Putting the statements together, we know that if angle ABC is 90 degrees, AB and BC are the sides adjacent to the 90 degree angle - the base and the height of the triangle. This means we can solve for area by plugging 5 and 13 into the area formula.
A = (1/2)*5*13
BOTH statements together are sufficient. The correct answer is C.
