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WXYZ is a parallelogram

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WXYZ is a parallelogram [#permalink] New post 13 Feb 2017, 05:52
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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
[Reveal] Spoiler: OA
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Joined: 07 Jun 2014
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GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
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Re: WXYZ is a parallelogram [#permalink] New post 14 Feb 2017, 15:38
Expert's post
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.
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Sandy
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Re: WXYZ is a parallelogram   [#permalink] 14 Feb 2017, 15:38
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