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In triangle PQR, if PQ = x, QR = x + 2, and PR = y, which of the three angles of triangle PQR has the greatest degree measure?
(1) y = x+ 3
(2) x = 2
(1) y = x+ 3
(2) x = 2
13 Aug 2012, 07:16
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SOLUTION
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.
Answer: A.
For more on this topic check Triangles chapter of Math Book: math-triangles-87197.html
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.
Answer: A.
For more on this topic check Triangles chapter of Math Book: math-triangles-87197.html
General Discussion
13 Aug 2012, 07:34
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IMO A
1) Sufficient: we have comparison of all 3 sides of triangle in terms of x (x= +ve). Angle opposite to x+3 will have greatest degree measure.
2) Insufficient: We don't know value of Y.
1) Sufficient: we have comparison of all 3 sides of triangle in terms of x (x= +ve). Angle opposite to x+3 will have greatest degree measure.
2) Insufficient: We don't know value of Y.
