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# In Triangle ABC, if AB = x, BC = y, and AC = x + y, which of

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Re: In Triangle ABC, if AB = x, BC = y, and AC = x + y, which of [#permalink]

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08 Jul 2012, 06:44
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15% (low)

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89% (01:30) correct 11% (00:00) wrong based on 28 sessions

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metallicafan wrote:
In Triangle ABC, if AB = x, BC = y, and AC = x + y, which of the three angles of Triangle ABC has the least degree measure?

(1) x = y + 1
(2) y = 4

I think there is a typo in this question.
We know that a rule in triangles theory is:
|Side 2 - Side 3| < Side 1 < Side 2 + Side 3

So, how can AC (x+y) be equal to AB (x) and BC (y)?

Source: http://www.gmathacks.com

You are right, the question is flawed. They just took and incorrectly rephrased question from OG, which is:

In Δ PQR, if PQ = x, QR = x + 2, and PR = y, which of the three angles of Δ PQR has the greatest degree measure?

Important properties of a triangle.
The shortest side is always opposite the smallest angle.
The longest side is always opposite the largest angle.

The length of any side of a triangle must be larger than the positive difference of the other two sides, but smaller than the sum of the other two sides.

(1) y = x + 3 --> PR is the longest side, hence opposite the largest angle PQR. Sufficient.
(2) x = 2 --> PQ=2 and QR=4 --> 2<PR<6. So, we cannot determine which side is the longest QR or PR. Not sufficient.

[Reveal] Spoiler: OA

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Re: In Triangle ABC, if AB = x, BC = y, and AC = x + y, which of   [#permalink] 08 Jul 2012, 06:44
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