Data Sufficiency

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.

IMO B

pls do let me knw the OA as this was discussed earlier in this forum but i guess OA was given

I think C should be correct.
1- If we know that base of the parallelogram is 10 then 1/2h*10 is 100 - h = 20
2- The angle is 45 degrees (issocelles right triangle) - hypotenuse 20sqrt3
combine and get - perimetr 20+40sqrt3

(1)We know the base and the height, but without an angle, we can't determine the sides relative to each other.

(2) We know an angle, but without info about the length of any one side, we can't know how far down the base the height hits, and therefore can't determine the length of any side.

Together ershovici is correct - we can determine the height using the area and the hypotenuse using the angle in the triangle.

grockit_jake wrote:(1)We know the base and the height, but without an angle, we can't determine the sides relative to each other.

(2) We know an angle, but without info about the length of any one side, we can't know how far down the base the height hits, and therefore can't determine the length of any side.

Together ershovici is correct - we can determine the height using the area and the hypotenuse using the angle in the triangle.

hi jake kindly check the attachment and explain where i am wrong

I attached another file, in which I edited your parallelogram

You were not wrong in your drawing, but you made the assumption that the height connected opposite points within the parallelogram.

I moved your lines out such that the horizontal lines are longer. This means there are 2 triangles that we can derive but an interior rectangle for which we have no information.

ershovici wrote:I think C should be correct.
1- If we know that base of the parallelogram is 10 then 1/2h*10 is 100 - h = 20
2- The angle is 45 degrees (issocelles right triangle) - hypotenuse 20sqrt3
combine and get - perimetr 20+40sqrt3

Dont get this : 1/2h*10 is 100 - h = 20

Given area of a parallelogram, we need to find perimeter.

From statement 1.
base = 10,

Area = base * height
100 = 10 * height
i.e. h = 10

Perimeter = 2(a+b) = 2(10 + b)

Statement 1 is insufficient.

From Statement 2.
We know the angle is 45
We have a formula for Area of parallelogram as

Area = ab sin@
100 = ab sin45

Insufficient

From 1 & 2
We get 100 = 10b* (1/1.14)
hence we can calculate permiter 2(a+b)

Ans is C

crazy4gmat wrote: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.

IMO E

Every Rhombus is a parallelogram, right ? so how would that effect this questuon ?