In triangle PQR, if PQ = x, QR = x + 2, and PR = y, which of the three

Question

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

Bunuel · Answer

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

SOURH7WK · Answer

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.

Aximili85 · Answer

A 
1) Gives correlation between all sides, X+3 is the longest side
2) Insufficient -> x = 2, 2nd side = 4, and 3rd side 2<y<6
So y could be 3 or 5  (3rd side always greater than difference of other 2 but less than sum)

madn800 · Answer

Buneul I believe that statement (2) should be interpreted as follows: firstly, if x=2 then PQ=x=2; also, QR= x+2=4. Now the possible values of the third side lie between (4-2=)2 and (4+2=)6 that is the third side PR can take the values 3,4 or 5. For (PQ,PR,QR)=(2,3,4) largest angle is P. Next for (2,4,4) angle P=Q=greatest. Lastly, for (2,5,4) largest angle is Q. As, we are getting three different answers this statement is clearly insufficient.

Bunuel · Answer

From my post above: (2) x = 2 --> PQ=2 and QR=4 --> 2

aeglorre · Answer

1) tells us the length relation among the three sides, so it's sufficient for us to know which angle has the greatest degree measure
2) tells us nothing about y and so it's insufficient..

We go with A

JeffTargetTestPrep · Answer

We start by sketching the triangle.

https://i.imgur.com/pwUDd5Q.png

We need to determine the angle with the greatest degree measure. Remember that the angle with the greatest measure is always opposite the side of greatest length.

Statement One Alone:

y = x + 3

Since we know that y = x + 3, we know that PR is the longest side of the triangle. Thus, we know that angle PQR, the angle opposite side PR, is the angle with the largest measure. Statement one is sufficient to answer the question. We can eliminate answer choices B, C, and E.

Statement Two Alone:

x = 2

Only knowing the value of x is not sufficient to answer the question because we don’t know the value of y.

The answer is A.

dave13 · Answer

Bunuel can you please rephrase the sentence below., cant understand it somehow

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.

Bunuel · Answer

If the two sides of a triangle are 8 and 6, then for the third side we'd have:

(8 - 6) < (third side) < (8 + 6)
2 < (third side) < 14

bumpbot · Answer

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In triangle PQR, if PQ = x, QR = x + 2, and PR = y, which of the three

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