Target question: What is the area of right triangle XYZ?

KEY CONCEPT: Area of triangle = (1/2)(base)(height)
So, to answer the target question, we need lengths of BOTH the base AND the height.

Statement 1: Side YZ is 9 inches long.
We have only 1 measurement. So, there's no way to determine the area of the triangle.
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: Side XZ is 15 inches long.
We have only 1 measurement. So, there's no way to determine the area of the triangle.
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
We still don't have enough information.
Consider the following 2 cases (which both satisfy the given conditions).

case a:

Here, the area = (1/2)(9)(12) = 54

case b:

Here, the area = (1/2)(9)(15)= 67.5
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer = E

Cheers,
Brent
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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?
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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?