what is the perimeter

Question

what is the perimeter?

kapslock · Answer

Area of the parallelogram = 1/2 x Base x Altitude.

From (1), 100 = 1/2 x 10 x Altitude. This gives altitude, but not the angle of the parallelogram. Thus the perimeter cant be determined.

From (2), One angle is 45 deg, the opposite is 45 too, and the two remainsin angles are 135 deg each. But this doesn't tell us the size of the sides to determine the parameter. Thus insufficient.

Combining,
We know the base and the altitude and the angles. (which angle is which doesn't matter). Thus the perimeter can be computed.

Hence C.

Dan · Answer

kapslock, 

Area = Base x Altitude (not 1/2)

from this, and given that base = height = 10, I couldn't get the exact dimensions for the perimeter...

sonaketu · Answer

Sin (45) = 10/(2nd Side)
=> 1/sqrt(2) = 10/(2nd side)
=> 2nd side = 10* sqrt(2)

Thus perimeter = 2*(10+10*sqrt(2))

chunjuwu · Answer

please explain, thanks :oops:

ashkg · Answer

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.

chunjuwu · Answer

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

ian7777 · Answer

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:

 https://www.integratedlearning.net/gmatclub/isosparallogram.gif

Dan · Answer

perfect drawing..now it makes sense..thanks!

chunjuwu · Answer

wonderful drawing, ian777, so interesting, isn't it?

Ozmba · Answer

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 ?

HowManyToGo · Answer

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.

what is the perimeter

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