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WXYZ is a parallelogram
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13 Feb 2017, 05:52
13 Feb 2017, 05:52
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Question Stats:
36% (00:15) correct
63% (00:26) wrong based on 11 sessions
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WXYZ is a parallelogram.
Quantity A |
Quantity B |
Diagonal WY |
Diagonal XZ |
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given
Re: WXYZ is a parallelogram
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14 Feb 2017, 15:38
14 Feb 2017, 15:38
Expert Reply
Explanation
Let a and b be the sides of the parallelogram and β be the angle in between a and b.
Formula of parallelogram diagonal in terms of sides and cosine β (cosine theorem). In this case β=100.
Diagonal XZ = \(\sqrt{a^2 + b^2 - 2ab cos(\beta)}\) =\(\sqrt{a^2 + b^2 - 2ab cos(100)}\) =\(\sqrt{a^2 + b^2 + 2ab cos(80)}\).
Diagonal WY = \(\sqrt{a^2 + b^2 - 2ab cos(\beta)}\) = \(\sqrt{a^2 + b^2 - 2ab cos(80)}\).
Thus clearly XZ is greater. Hence option B is correct.
Alternatively you can just remember that in a parallogram the diagonal opposite to the larger angle is greater in length than the other one.
Let a and b be the sides of the parallelogram and β be the angle in between a and b.
Formula of parallelogram diagonal in terms of sides and cosine β (cosine theorem). In this case β=100.
Diagonal XZ = \(\sqrt{a^2 + b^2 - 2ab cos(\beta)}\) =\(\sqrt{a^2 + b^2 - 2ab cos(100)}\) =\(\sqrt{a^2 + b^2 + 2ab cos(80)}\).
Diagonal WY = \(\sqrt{a^2 + b^2 - 2ab cos(\beta)}\) = \(\sqrt{a^2 + b^2 - 2ab cos(80)}\).
Thus clearly XZ is greater. Hence option B is correct.
Alternatively you can just remember that in a parallogram the diagonal opposite to the larger angle is greater in length than the other one.
gmatclubot
Re: WXYZ is a parallelogram [#permalink]
14 Feb 2017, 15:38
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