minwoswoh wrote:
What is the area of right triangle XYZ?
(1) Side YZ is 9 inches long.
(2) Side XZ is 15 inches long.
Question Stem Analysis:We need to determine the area of right triangle XYZ. We are not provided with any other information in the question stem.
Statement One Alone:\(\Rightarrow\) Side YZ is 9 inches long.
Without knowing anything about the remaining two sides of the triangle, we cannot determine its area. Statement one alone is not sufficient.
Eliminate answer choices A and D.
Statement Two Alone:\(\Rightarrow\) Side XZ is 15 inches long.
Without knowing anything about the remaining two sides of the triangle, we cannot determine its area. Statement two alone is not sufficient.
Eliminate answer choice B.
Statements One and Two Together:We should be careful not to assume that this is a 9 - 12 - 15 right triangle, because we don't know whether the side of length 15 is the hypotenuse.
If XZ is the hypotenuse, then we have a 9 - 12 - 15 right triangle, which means its area is 1/2 * 9 * 12 = 54.
If XZ is not the hypotenuse, then the area of the triangle is 1/2 * 9 * 15 = 67.5.
Since there is more than one possible value for the area of the triangle, statements one and two together is not sufficient.
Answer: E _________________