Sorry , my question was not correclty formulated.

i somewhere read that trapezoid is a special type of parallelogram with one pare of parallel sides. Could that be right?

regarding the problem got question:

cant parallelogram be trapezoid with equal sides ? (in that case the area of trapezoid will be totally different and the answer will be E )

Shouldn't the answer be (B)

Let's say base = Height = x (because given 45 degree condition, we end up with an isosceles right triangle as shown above)
then question stem says x*x = 100 which means that x= 10 and the other side = x*root(2) (as per isosceles right triangle prop.)

Then we have P = 2( 10 + 10* root(2))

Why need A when we can get the same info from only statement 2?

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.

Statement 1
base = 10
given
area of a parallelogram = 100
base x height = 100
so, height = 10
height does not give the side of the parallelogram...
height is only equal to side if the parallelogram is a rectangle or a square
Insufficient
Statement 2
one of the angle of the parallelogram is 45 degs.
This does not say anything about sides.
insufficient

combining we can use the Pythagoras theorem to find the side...
so sufficient
Answer C

Let parallelogram be ABCD. Base AD = 10, height BX = 10 and the angle BAD = 45 degrees. This would mean that when you draw the hight from B it will meat the base at point D (D and X will coincide). So the height will be the diagonal too. AB and CD will become hypotenuses and will be equal to \(10\sqrt{2}\).

\(P=20+20\sqrt{2}\).

Hope it's clear.

I am unable to understand when the angle is 45 degree How X will coincide with D. Because angle is 45 degree not 90 degree. Can you please draw the Figure also. Thanks!

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.

I thought A, because if the base is 10, the side has to be 10, because Area is 10. Therefore perimeter is 40. Regardless if this is a rhombus or not. B is insuffic, gives no details for lengths of sides.

(Maybe I am confusing what a base is? I am interpreting it as one of the sides.)

The OA is C. Not sure why, can someone please explain?

If the area of a parallelogram is 100, what is the perimeter of the parallelogram?

Given: \(Area=base*height=100\). Q: \(P=2b+2l=?\) (b - base, l - leg )

(1) The base of the parallelogram is 10 --> \(base=height=10\). Infinite variations are possible. Look at the diagram (let the distance between two horizontal and vertical points be 10): all 4 parallelograms have \(base=height=10\) but they have different perimeter. Not sufficient. Side notes: \(l\geq{10}\), when \(l=10=h\) we would have the square (case #3 on the diagram) and \(P=40\) (smallest possible perimeter), maximum value of perimeter is not limited.

(2) One of the angles of the parallelogram is 45 degrees. Clearly insufficient. But from this statement height BX and AX will make isosceles right triangle: \(height=BX=AX\).

(1)+(2) As from 2 we have that \(height=BX=AX\) and from (1) we have that \(base=height=10\) --> \(AX=base=AD=10\) --> X and D coincide (case #4 on the diagram) --> leg (AB) becomes hypotenuse of the isosceles right triangle with sides equal to 10 --> \(AB=10\sqrt{2}\) --> \(P=20+20\sqrt{2}\). Sufficient.

Answer: C.

Hope it's clear.

Bunuel/Anyone
Why not A alone is sufficient
being known 2 sides are 10 it means angles are also same .also as height BD is making 90 deg. means the other 2 angles are 45 deg each
fig. attached)
Thus making A as ans choice

Thanks

Bunuel/Anyone
Why not A alone is sufficient
being known 2 sides are 10 it means angles are also same .also as height BD is making 90 deg. means the other 2 angles are 45 deg each
fig. attached)
Thus making A as ans choice

Thanks

If the area of a parallelogram is 100, what is the perimeter of the parallelogram?

Given: \(Area=base*height=100\). Q: \(P=2b+2l=?\) (b - base, l - leg )

(1) The base of the parallelogram is 10 --> \(base=height=10\). Infinite variations are possible. Look at the diagram (let the distance between two horizontal and vertical points be 10): all 4 parallelograms have \(base=height=10\) but they have different perimeter. Not sufficient. Side notes: \(l\geq{10}\), when \(l=10=h\) we would have the square (case #3 on the diagram) and \(P=40\) (smallest possible perimeter), maximum value of perimeter is not limited.

(2) One of the angles of the parallelogram is 45 degrees. Clearly insufficient. But from this statement height BX and AX will make isosceles right triangle: \(height=BX=AX\).

(1)+(2) As from 2 we have that \(height=BX=AX\) and from (1) we have that \(base=height=10\) --> \(AX=base=AD=10\) --> X and D coincide (case #4 on the diagram) --> leg (AB) becomes hypotenuse of the isosceles right triangle with sides equal to 10 --> \(AB=10\sqrt{2}\) --> \(P=20+20\sqrt{2}\). Sufficient.

Answer: C.

Hope it's clear.

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.

We know from 2 that AD=BD, hence and hence we can find out base of the //gm , and we can find of the other side using pythagoras on sin45. hence finding the perimeter. I am unable to understand that how is B insufficient?

If the area of a parallelogram is 100, what is the perimeter of the parallelogram?

Given: \(Area=base*height=100\). Q: \(P=2b+2l=?\) (b - base, l - leg )

(1) The base of the parallelogram is 10 --> \(base=height=10\). Infinite variations are possible. Look at the diagram (let the distance between two horizontal and vertical points be 10): all 4 parallelograms have \(base=height=10\) but they have different perimeter. Not sufficient. Side notes: \(l\geq{10}\), when \(l=10=h\) we would have the square (case #3 on the diagram) and \(P=40\) (smallest possible perimeter), maximum value of perimeter is not limited.

(2) One of the angles of the parallelogram is 45 degrees. Clearly insufficient. But from this statement height BX and AX will make isosceles right triangle: \(height=BX=AX\).

(1)+(2) As from 2 we have that \(height=BX=AX\) and from (1) we have that \(base=height=10\) --> \(AX=base=AD=10\) --> X and D coincide (case #4 on the diagram) --> leg (AB) becomes hypotenuse of the isosceles right triangle with sides equal to 10 --> \(AB=10\sqrt{2}\) --> \(P=20+20\sqrt{2}\). Sufficient.

Answer: C.

Hope it's clear.