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605-655 (Medium)|   Geometry|      
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If the area of a parallelogram is 100, what is the perimeter 13 Oct 2019, 03:58
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Bunuel
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Hi, Bunuel,
I really appreciate your effort to help us. Finally after your explanation, I got the answer (since I imagined what kind of parallelogram the problem was talking about.
But, based on what assumptions, you deduce that parallelogram needs to be the way you described (diagonal equal to height)?
Attachment:
PointLatticeParallelograms_1000.gif
If the area of a parallelogram is 100, what is the perimeter of the parallelogram?

Given: \(Area=base*height=100\). Q: \(P=2b+2l=?\) (b - base, l - leg )

(1) The base of the parallelogram is 10 --> \(base=height=10\). Infinite variations are possible. Look at the diagram (let the distance between two horizontal and vertical points be 10): all 4 parallelograms have \(base=height=10\) but they have different perimeter. Not sufficient. Side notes: \(l\geq{10}\), when \(l=10=h\) we would have the square (case #3 on the diagram) and \(P=40\) (smallest possible perimeter), maximum value of perimeter is not limited.

(2) One of the angles of the parallelogram is 45 degrees. Clearly insufficient. But from this statement height BX and AX will make isosceles right triangle: \(height=BX=AX\).

(1)+(2) As from 2 we have that \(height=BX=AX\) and from (1) we have that \(base=height=10\) --> \(AX=base=AD=10\) --> X and D coincide (case #4 on the diagram) --> leg (AB) becomes hypotenuse of the isosceles right triangle with sides equal to 10 --> \(AB=10\sqrt{2}\) --> \(P=20+20\sqrt{2}\). Sufficient.

Answer: C.
Attachment:
m10-31.png

Hope it's clear.
Show more

We know from 2 that AD=BD, hence and hence we can find out base of the //gm , and we can find of the other side using pythagoras on sin45. hence finding the perimeter. I am unable to understand that how is B insufficient?
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If the area of a parallelogram is 100, what is the perimeter 10 Jul 2020, 06:15
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rush123
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Hi, Bunuel,
I really appreciate your effort to help us. Finally after your explanation, I got the answer (since I imagined what kind of parallelogram the problem was talking about.
But, based on what assumptions, you deduce that parallelogram needs to be the way you described (diagonal equal to height)?
Attachment:
PointLatticeParallelograms_1000.gif
If the area of a parallelogram is 100, what is the perimeter of the parallelogram?

Given: \(Area=base*height=100\). Q: \(P=2b+2l=?\) (b - base, l - leg )

(1) The base of the parallelogram is 10 --> \(base=height=10\). Infinite variations are possible. Look at the diagram (let the distance between two horizontal and vertical points be 10): all 4 parallelograms have \(base=height=10\) but they have different perimeter. Not sufficient. Side notes: \(l\geq{10}\), when \(l=10=h\) we would have the square (case #3 on the diagram) and \(P=40\) (smallest possible perimeter), maximum value of perimeter is not limited.

(2) One of the angles of the parallelogram is 45 degrees. Clearly insufficient. But from this statement height BX and AX will make isosceles right triangle: \(height=BX=AX\).

(1)+(2) As from 2 we have that \(height=BX=AX\) and from (1) we have that \(base=height=10\) --> \(AX=base=AD=10\) --> X and D coincide (case #4 on the diagram) --> leg (AB) becomes hypotenuse of the isosceles right triangle with sides equal to 10 --> \(AB=10\sqrt{2}\) --> \(P=20+20\sqrt{2}\). Sufficient.

Answer: C.
Attachment:
m10-31.png

Hope it's clear.

We know from 2 that AD=BD, hence and hence we can find out base of the //gm , and we can find of the other side using pythagoras on sin45. hence finding the perimeter. I am unable to understand that how is B insufficient?
Show more
Because we don't have any specific value of Base and Height. 100 area can have many possible values (100, 1) (25,4) (20,5) ... And so on. That's why it's insufficient.

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If the area of a parallelogram is 100, what is the perimeter 29 Aug 2021, 23:00
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Hi Everyone,

I did try to understand all the other explanations.

However I am still not able to solve a scenario based on statement II wherein if we assume angle ABC to be 45 degrees. (Considering any angle can be 45)

In case of the above assumption I suppose we cannot get a 45-45-90 triangle.

Please let me know what is the flaw in my above assumption.
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If the area of a parallelogram is 100, what is the perimeter 30 Aug 2021, 05:15
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Applicant4991
Hi Everyone,

I did try to understand all the other explanations.

However I am still not able to solve a scenario based on statement II wherein if we assume angle ABC to be 45 degrees. (Considering any angle can be 45)

In case of the above assumption I suppose we cannot get a 45-45-90 triangle.

Please let me know what is the flaw in my above assumption.
Show more
From statement 1. It's given that the height of parallelogram is 10 (since base is 10) but we can't determine the length of slant height of parallelogram without knowing anything about the angles.
A is not sufficient.

Statement B states one of the angle of parallelogram is 45°
Since there are two equal acute angles in parallelogram and 2 equal obtuse angles. Here B and D are acute angles of 45°
You can see and analyze which angle will be acute of obtuse for this.
Back to question.
The length of base could be 100 and height 1 or vice versa or both could be 10 each.
There are 3 possible answers here.
Not sufficient.

Adding both statements together,
We get this diagram type structure.
Pardon for my screen scribbling. It's definitely not good. But I hope you get the diagram.

We can analyse the slant height of parallelogram using right angle triangle property.
That's why answer is C

Hope this helps.

Posted from my mobile device
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IMG_20210830_174424.jpg
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If the area of a parallelogram is 100, what is the perimeter 03 Dec 2021, 03:11
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here is a video answer for anyone interested! :)
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If the area of a parallelogram is 100, what is the perimeter 26 Oct 2023, 09:34
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