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Each side of a certain parallelogram has length 6. if the

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Each side of a certain parallelogram has length 6. if the [#permalink] New post 26 Jan 2008, 10:31
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Each side of a certain parallelogram has length 6. if the area of the parallelogram is 18.
which of the following is the measure of one of its angles?

A. 30
B. 45
C. 60
D. 90
E.120

Please explain
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Re: PS;set24;Q31;Parallelogram [#permalink] New post 26 Jan 2008, 10:48
Since it is a PS question, I would pick D on exam.
sides are equal so it most probably a rhomb. if i recall correctly, the area of a rhomb is half the product of its diagonals? d1d2 = 18*2 = 36. perhaps diagonals are equal in lenght (sqrt 36 = 6).

so we have two equilateral traingles. where angles are equal to 60 degrees.
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Re: PS;set24;Q31;Parallelogram [#permalink] New post 26 Jan 2008, 11:44
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A

Area=h*a

18=6*h ==> h=3
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Re: PS;set24;Q31;Parallelogram [#permalink] New post 26 Jan 2008, 12:50
A too.

We know that Area= base * height. If the Area=18, and base = 6, height must be 3, that is, the angle must be 30º.
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Re: PS;set24;Q31;Parallelogram [#permalink] New post 27 Jan 2008, 00:56
OA is A. walker thanks again for you efforts. +1
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Re: PS;set24;Q31;Parallelogram [#permalink] New post 28 Jan 2008, 08:40
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Given each side is 6 and area is 18. We can find the altitude, ie: alt = 18/6 = 3.
Now we have a triangle with one side as 6, the alt as 3, and the base which we don't know.

Using Pythagoras theorem, 6^2 = 3^2 + Base^2 => Base = 3V3
So, the sides are now 3*1, 3*V3, 3*2 => 1:V3:2, which is a 30-60-90 triangle.

Hence the angle that we know is 30, which forms a side of the parallelogram.
Ans: A.
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Re: PS;set24;Q31;Parallelogram [#permalink] New post 03 Mar 2008, 11:37
Sleepless wrote:
Given each side is 6 and area is 18. We can find the altitude, ie: alt = 18/6 = 3.
Now we have a triangle with one side as 6, the alt as 3, and the base which we don't know.

Using Pythagoras theorem, 6^2 = 3^2 + Base^2 => Base = 3V3
So, the sides are now 3*1, 3*V3, 3*2 => 1:V3:2, which is a 30-60-90 triangle.

Hence the angle that we know is 30, which forms a side of the parallelogram.
Ans: A.

very nice :-D
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Re: PS;set24;Q31;Parallelogram [#permalink] New post 03 Mar 2008, 11:46
6*6*sin(alpha) = 18 -> sin(alpha) = 1/2 -> alpha = 30 -> A
Re: PS;set24;Q31;Parallelogram   [#permalink] 03 Mar 2008, 11:46
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