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# the area of a parallelogram is 100. what is the perimeter of

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Intern
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the area of a parallelogram is 100. what is the perimeter of [#permalink]  30 May 2007, 15:54
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the area of a parallelogram is 100. what is the perimeter of the parallelogram ?

1) the base of the parallelogram is 10
2) one of the angles of the parallelogram is 45 degree
Director
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Re: DS question- parallelogram [#permalink]  30 May 2007, 17:09
hsk wrote:
the area of a parallelogram is 100. what is the perimeter of the parallelogram ?

1) the base of the parallelogram is 10
2) one of the angles of the parallelogram is 45 degree

I'm going for E. 1) we can figure the height (10(h)=100, h=10) but not the measure of the sides adjacent the base. 2) the parallelogram is made of 2 45 degree angles and 2 135 degree angles. perhaps if we knew whether the 45 degree angle or the 135 degree angle corresponded to the base we could figure the measure of the other 2 sides.
Intern
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its (C)
Knowing the height of the parallelogram and one of the angles, using trigonometry it is possible to work out the length of the side of the parallelogram. And therefore the perimeter.
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Re: DS question- parallelogram [#permalink]  30 May 2007, 18:32
hsk wrote:
the area of a parallelogram is 100. what is the perimeter of the parallelogram ?

1) the base of the parallelogram is 10
2) one of the angles of the parallelogram is 45 degree

Always Remember and memorize:

Opposite angles of a parallelogram are congruent ( Equal )

Consecutive angles of a parallelogram are supplementary. ( sum is equal to 180deg )

Area of the parallelogram is = BASE X ALTITUDE

From ( i ), we know only the base but not the altitude ( height ) and thus we can't find the area of the parallelogram.

From ( ii ) we know only the angle and using the properties that opposite angles are equal and consecutive angles are supplementary, we can conclude that the four angles are ;

45deg, 135deg, 45deg, and 135deg.

If we combine ( i ) and ( ii );

we know the angles and we know the base, but there is no way to find the altitude ( height ).

Thus we can't determine the area with the given information.

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Re: DS question- parallelogram [#permalink]  30 May 2007, 18:52
hsk wrote:
the area of a parallelogram is 100. what is the perimeter of the parallelogram ?

1) the base of the parallelogram is 10
2) one of the angles of the parallelogram is 45 degree

Given information is area of a parallelogram= 100=length of altitude * lenght of base

What is the perimeter i.e. what is the length of base and altitude
1. base is given and area we know,sufficient to know perimeter
2. Angle is 45 degree,doesn't help to find length of altitude or base

Director
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Re: DS question- parallelogram [#permalink]  30 May 2007, 19:07
hsk wrote:
the area of a parallelogram is 100. what is the perimeter of the parallelogram ?

1) the base of the parallelogram is 10
2) one of the angles of the parallelogram is 45 degree

Sorry, the answer is indeed C
Intern
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can someone please explain how the angle helps you figure out the altitude?

I thought the formula was the same as a rectangle and thats why I picked A, but the right answer is C
Intern
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From (1),
For a parallelogram,
A = B*H
=> H = 10

From (2),
Since H = B,
sin 45 = 10/L
=> L = 10/sin45

From information obtained from both statements, we can calculate the perimeter of the parallelogram. Diagram below should make things clearer.
Attachments

New Picture.png [ 1.98 KiB | Viewed 814 times ]

Intern
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thanks waldeck, that does the trick!!!
Manager
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HSK, are you sure the answer is C?? Where did you get this problem from?
Intern
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yes i am sure,

its from one of the challenges
Manager
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I quess I'm doing something wrong here:

If the base is 10 and the area is 100 then the height must be 10. Based on the first statement I know that we have a right isosceles triangle. Hence the angles of the paralleloram are 45 - 135 -45 -135.

St.#2 is just the opposite. The answer looks like D to me.
Intern
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Hayabusa,
It is not correct to assume that we get a right isosceles triangle just from statement (1).
As an illustration, see below figures (a) where b=h.

Similarly, we cannot assume b=h just from statement (2)
Refer to figures (b).

Therefore it is necessary to have both statements to get the answer.
Attachments

New Picture (1).png [ 2.74 KiB | Viewed 787 times ]

Intern
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The approach - Draw a diagonal, we get two congruent triangles.
From Statment (1) we know that base = 10
From congruency of triangles we get that the adjacent side is also = 10
(Sides opp equal angles are equal).
Thus we can find the perimeter.
Director
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waldeck55 wrote:
From (1),
For a parallelogram,
A = B*H
=> H = 10

From (2),
Since H = B,
sin 45 = 10/L
=> L = 10/sin45

From information obtained from both statements, we can calculate the perimeter of the parallelogram. Diagram below should make things clearer.

Hi,

Could you please tell me how did you post the image of the parallelogram in your post?

The new png file which you have posted and is visible. How do you attach that one?
Director
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So do we assume that a parallelogram always break down into 2 right angles and a rectangle or simply 2 triangles? If not, I don't see why the parallelogram couldn't have been orientated this way (attached)
Attachments

diagram1.doc [51 KiB]

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