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

Question

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

GMAT TIGER · Answer

I got C.

p = 20 + 20 sqrt 2

ashkrs · Answer

C

1. Not suff . We can only know the height ie 100/10 = 10

2. Not suff . T

Combining we can find length of other parallel side ie 10sqrt2.

bmwhype2 · Answer

why cant we infer this from A?

 https://www.integratedlearning.net/gmatclub/isosparallogram.gif

GMAT TIGER · Answer

do you know one (two) of the angle of parrellogram is 45 deg?

bmwhype2 · Answer

isnt the height always perpendicular to the base? thus forming an isosceles right triangle?

Whatever · Answer

My answer is A
Actually, I was surprised that you were considering C ...

S = a * h

I. Suff: a*h = 100, a = 10 --> h = 10 --> we can infer b from 1:1:sqrt(2) triangle
P = 2*(a + b)

GMAT TIGER · Answer

you can draw a parallellogram with two opposit angles 1-1 (or 10-10, 100-100) and rest 179-179 (170-170, 80-80). do you still think that, it is an issoceles triangle if we draw a perpendicular on the base?

only opposit sides are equal not the adjacent sides. we know this facto nly after going through st 1 and 2.

CaspAreaGuy · Answer

you are right. the answer is D.

(1) find height and then hypotenuse SUFF

(2) 45 degrees gives an isosles triangle. since we know that area formula is heigh*base and it equals 100. in isosles triangle two sides are equal and hence one of them is sqrt 100. SUFF

good question!

Whatever · Answer

CaspAreaGuy , but what if the base of parallelogram = 100 and height = 1?
Then, the triangle has legs 1:1:sqrt(2) and hence the P = 100*2 + sqrt(2) * 2 = 200 + 2*sqrt(2)?

CaspAreaGuy · Answer

but if the base is 100 and height is 1, will it be an isosles triangle? didn't get your point, sorry.

Whatever · Answer

Consider base = 100 and height = 1
..---------------------------
/ | ............................. /
---------------------------

There is a triangle from the left formed with the height = 1, and with the angles 45-90 (hence height forms right angle)-45 --> triangle is isosceles

CaspAreaGuy · Answer

I got your point. Thank you. Traingle can still be isosless even if the height =100

alexperi · Answer

My answer is C.
You need both.
Square is a parallelogram with a perimeter of 40 
So you need B information to give you the perimeter 20+20sqrt2

bmwhype2 · Answer

alright i figured it out.

we can have that figure, or we can have a square. if we have that figure the sides are 10sqrt2 and 10. If we have a square, we have 10 and 10.

alexperi · Answer

No.
Square gives the minimum perimeter

so 
1) 90 degrees square looks like this
----------


----------


2) 70 degrees looks like this
 ----------


----------

3) 45 degrees looks like this
 ----------


----------

4)
 35 degrees looks like this
 ----------


----------

The perimeter could be infinite as the degrees approach 0
This is why you need both
45degrees gives you isosceles both on the base on the height and don't provide enough info in finding the perimeter

alexperi · Answer

Aaaaaa spaces are excluded

lape · Answer

so what's the correct answer?

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

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