Parallelogram

[crackgmat007]

If 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 degrees.

OA - C can someone solve the problem and find the permiter?

[xcusemeplz2009]

i think 2nd is sufficient ,
IMO ans should be (b)

perimeter=20(1+sqrt2)

[sanjana]

IMO : C is the correct answer

Consider the figure attatched

Given : Area of the parallelogram is 100

We know that Area of a paralleogram is (bxh)

Now bh = 100 (given)
We have to find : 2(b+l) as opposite sides of a paralleogram are equal.

Statement 1 :
------------
b=10 (AB)

hence, h=10

This tells us nothing about the length. hence insufficient.

Statement 2 :
-------------
One Angle is 45,say angle C.Therfore angle A is also 45 as opposite sides and angles of a parallelogram are equal.

But with no information about the sides we cannot find the perimeter

Hence,insufficient

Combining the 2 statements,

When h=10
And angle DEA is 90,therefore DAE is a 45-45-90 right triangle
Hence DA = l = 5sqrt(2)

Therefore perimeter = 2(10+5sqrt(2))

Hence,C

Hope this helps.

[crackgmat007]

Combining the 2 statements,

When h=10
And angle DEA is 90,therefore DAE is a 45-45-90 right triangle

I followed the same steps. Since DEA is a 45-45-90 right triangle ie 1:1: sqrt 2, which means that hieght is same as and the leg ie DE = AE = 10. But question states that base is 10. Looks like I am missing something?

Hence DA = l = 5sqrt(2)

Can you explain 'DA = l'

[sanjana]

I meant the letter L to stand fr length.

[xcusemeplz2009]

IMO : C is the correct answer

Consider the figure attatched

Given : Area of the parallelogram is 100

We know that Area of a paralleogram is (bxh)

Now bh = 100 (given)
We have to find : 2(b+l) as opposite sides of a paralleogram are equal.

Statement 1 :
------------
b=10 (AB)

hence, h=10

This tells us nothing about the length. hence insufficient.

Statement 2 :
-------------
One Angle is 45,say angle C.Therfore angle A is also 45 as opposite sides and angles of a parallelogram are equal.

But with no information about the sides we cannot find the perimeter

Hence,insufficient

Combining the 2 statements,

When h=10
And angle DEA is 90,therefore DAE is a 45-45-90 right triangle
Hence DA = l = 5sqrt(2)

Therefore perimeter = 2(10+5sqrt(2))

Hence,C

Hope this helps.

from statement 2
if one angle is 45 then tan(45)=h/b
i.e h/b=1(bcoz tan45=1)
i.e h=b
area of llgm= b*h=100
or b^2=100
hence b=h=10
in tri DAE L^2=b^2+h^2=2b^2=bsqrt2=10sqrt2
perimeter=2(10+10sqrt2)

i am not getting where i am wrong

[sanjana]

Sorry for the last post..
What we both we missing I think was the way we drew the Diagram.
Refer to the new One attatched.

Now If angle B = 45
Then since DA and BC are parallel, angle DAE is also 45. Therefore now DE = AE = 10 and hence AD = 5 sqrt 2

Then we have base 10 and width 5 sqrt 2,so we can find the perimeter.

Agree?? :

[crackgmat007]

Actually, if the question were to say that one pair of the sides are parallel, I do agree with your solution.

Just to reconfirm the definition of parallelogram, got something on the internet.

https://www.mathopenref.com/parallelogram.html

Problem is poorly written? Experts, do you agree?

[crackgmat007]

Anyone?

[umaa]

Actually, if the question were to say that one pair of the sides are parallel, I do agree with your solution.

Just to reconfirm the definition of parallelogram, got something on the internet.

https://www.mathopenref.com/parallelogram.html

Problem is poorly written? Experts, do you agree?

Parallelogram means, opposite sides are parallel and equal in length. I don't see anything wrong in the question.

[umaa]

Sorry for the last post..
What we both we missing I think was the way we drew the Diagram.
Refer to the new One attatched.

Now If angle B = 45
Then since DA and BC are parallel, angle DAE is also 45. Therefore now DE = AE = 10 and hence AD = 5 sqrt 2

Then we have base 10 and width 5 sqrt 2,so we can find the perimeter.

Agree?? :

Sanjana,
AD is 10 sqrroot(2). AD is the diagonal of both AE and DE. A : A : A sqrrot(2)