What is the area of right triangle XYZ?

Hi there,

I found this question really tricky.

You can see that if the right answer is E, the reasoning obviously implies that even combining both statements you don´t have sufficient information to answer the question. As for this problem, this means that:
- EITHER XZ is the hypotenuse and therefore XY is 12 (the magic Pythagorean triple we all learnt!)
- OR XZ is not the hypotenuse and therefore XY is actually the hypotenuse. This would be written as 9^2 + 15^2 = XY^2. Therefore, XY = \(\sqrt{306}\) = 17.5 approx.

Both options yield to different areas for the triangle. Hence, E.

My confusion is the following:
If the question stem states that we have a right triangle XYZ, doesn´t that imply that Y = 90º (the central letter = 90º)? In other words, doesn´t that imply that YZ and YX MUST BE the legs?

Thanks for the explanation!
+1 for you

Can we also think of it like, they said it was a right angle triangle, but we don't know if it's a 30-60-90 or a 45-45-90 triangle. Would that also be a factor we can consider in this question?

Such a sly Question , got it wrong !!!

Hi BrentGMATPrepNow, a bit confused with this one that given XZ is 15 inches long but in case b diagram is 15 = YZ and not XZ?
Both statements combined we can say that third side is 12. Therefore shouldn't this fixed the longest length is 15 therefore make it C? Not sure what did I miss here? Thanks Brent

I made a mistake with the second graphic.
I have not replaced it.
Please check out my new response.

Thanks for the heads up! ! Kudos for you!!!!

Cheers,
Brent

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

Thanks Brent BrentGMATPrepNow

Great explanation. Thanks Scott ScottTargetTestPrep

Sure thing!

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