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Re: what is the perimeter [#permalink]
Sin (45) = 10/(2nd Side)
=> 1/sqrt(2) = 10/(2nd side)
=> 2nd side = 10* sqrt(2)

Thus perimeter = 2*(10+10*sqrt(2))
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Re: what is the perimeter [#permalink]
sonaketu wrote:
Sin (45) = 10/(2nd Side) hi, this is so weird. one side of the isosceles triangle equals the base and the altitude. But the base should be greater than the side. How could?
=> 1/sqrt(2) = 10/(2nd side)
=> 2nd side = 10* sqrt(2)

Thus perimeter = 2*(10+10*sqrt(2))


please explain, thanks :oops:
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Re: what is the perimeter [#permalink]
chunjuwu wrote:
sonaketu wrote:
Sin (45) = 10/(2nd Side) hi, this is so weird. one side of the isosceles triangle equals the base and the altitude. But the base should be greater than the side. How could?
=> 1/sqrt(2) = 10/(2nd side)
=> 2nd side = 10* sqrt(2)

Thus perimeter = 2*(10+10*sqrt(2))


please explain, thanks :oops:


Here he means side2 as the hypotenuse.
In this isosceles trigangle the base and altitude are same and lesser than the hypotenuse = side2.

Also the base of the triangle is not the same as the base of the parallelogram.
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Re: what is the perimeter [#permalink]
ashkg wrote:
chunjuwu wrote:
sonaketu wrote:
Sin (45) = 10/(2nd Side) hi, this is so weird. one side of the isosceles triangle equals the base and the altitude. But the base should be greater than the side. How could?
=> 1/sqrt(2) = 10/(2nd side)
=> 2nd side = 10* sqrt(2)

Thus perimeter = 2*(10+10*sqrt(2))


please explain, thanks :oops:


Here he means side2 as the hypotenuse.
In this isosceles trigangle the base and altitude are same and lesser than the hypotenuse = side2.

Also the base of the triangle is not the same as the base of the parallelogram.


HI, I supposed : altitude of the isosceles triangle = the altitude of the parallelogram =10. And the isosceles triangle is in fact a right triangle.
so, each base of the isosceles will be 10, and the hypotenus which is the another side of the parallelogram is 10 sqrt(2).

the question is that the base of the isosceles should be smaller than the base of the parallelogram. But..... they are both 10.

following is my draw
Am I wrong? :roll: thanks
Attachments

image001.gif
image001.gif [ 2.11 KiB | Viewed 857 times ]

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Re: what is the perimeter [#permalink]
It's definately C, and there's nothing wrong with it. We just need to see what's going on exactly. the parellelogram is made of two 45-45-90 triangles, each area 50:

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Re: what is the perimeter [#permalink]
perfect drawing..now it makes sense..thanks!
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Re: what is the perimeter [#permalink]
wonderful drawing, ian777,

so interesting, isn't it? :P
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Re: what is the perimeter [#permalink]
ian7777 wrote:
It's definately C, and there's nothing wrong with it. We just need to see what's going on exactly. the parellelogram is made of two 45-45-90 triangles, each area 50:



Base = 10

One angle = 45 Degrees

In Parallelogram opposite angles are equal ..so there are 2*45 Degrees

sum of all angles = 360

then 2*45 + 2x = 360

which gives each other as 135 Degrees

Ian can u please tell me how do we break the other two into 90 and 45 ?
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Re: what is the perimeter [#permalink]
Dan wrote:
what is the perimeter?



C.

In Geometry DS , as long as we are able to draw the required figure "data is sufficient" without bothering about how!

with A. There are infinite ways to parallelograms with 100 as an area, as long as the height is 10 units.( parallelograms with varying slants from 1 to 179 degrees)

with B, there is only one of such parallelograms wich has an angle 45 to the base.

HMTG.



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