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If sides of a quadrilateral X are integers, then is X a square?

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Bunuel
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If sides of a quadrilateral X are integers, then is X a square? [#permalink] New post   11 Jun 2020, 02:55
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If sides of a quadrilateral X are integers, then is X a square?

(1) Area of X is 324
(2) Areas of the triangles formed by the intersection of the diagonals of X are equal.


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Re: If sides of a quadrilateral X are integers, then is X a square? [#permalink] New post   11 Jun 2020, 06:17
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Bunuel wrote:
If sides of a quadrilateral X are integers, then is X a square?

(1) Area of X is 324
(2) Areas of the triangles formed by the intersection of the diagonals of X are equal.


Using Statement 1, the quadrilateral could be a square with dimensions 18x18, or could be a rectangle with dimensions 1x324, among other possibilities.

Statement 2 is true of every rectangle (square or not) -- if you divide a rectangle into four triangles by drawing diagonals, the area of each triangle will be LW/4. So Statement 2 gives no useful information at all, and the answer is E.
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Re: If sides of a quadrilateral X are integers, then is X a square? [#permalink] New post   11 Jun 2020, 11:01
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Bunuel wrote:
If sides of a quadrilateral X are integers, then is X a square?

(1) Area of X is 324
(2) Areas of the triangles formed by the intersection of the diagonals of X are equal.



Statement 1: Area of X is 324.

Now 324 = 18* 18.
So X could very well be a square.

But the dimensions of X could also be : 36*9 or 54*6. In this case X will be a rectangle.
So we cannot be sure of the shape of X.

So Insufficient.

Statement 2: Areas of the triangles formed by the intersection of the diagonals of X are equal.
The above statement again holds true for both square & rectangle.

So Insufficient.


Statement 1 + Statement 2: Even after combining both statements, we still wont have sufficient information as to whether X is a square or a rectangle.

So Answer Is E.
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Re: If sides of a quadrilateral X are integers, then is X a square? [#permalink] New post   11 Jun 2020, 11:17
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sides of quad. X = integers
Is X = square?

Statement 1: Area of X = 324=2*162 = 2*81 = 2*2*3*3*3*3 , which is perfect square
It means X is square or triangle
Not Sufficient

Statement 2: Area of tri. formed by intersection of diagonal X is equal
It means X will be rectangle or square
Not Sufficient

Statement 1 & Statement 2: Not sufficient

Answer : E
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Re: If sides of a quadrilateral X are integers, then is X a square? [#permalink] New post   12 Jun 2020, 00:31
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If sides of a quadrilateral X are integers, then is X a square?

(1) Area of X is 324

-- Area of a quadrilateral doesnot have a relation Insufficient

(2) Areas of the triangles formed by the intersection of the diagonals of X are equal.

-- It can be Rhombus also so Insufficient

combining 1 and 2 also Insufficient
Hence ans E
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Re: If sides of a quadrilateral X are integers, then is X a square? [#permalink] New post   13 Jun 2020, 23:53
Kindly see the attachment.
Both are insufficient.
E
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1.PNG [ 30.58 KiB | Viewed 1778 times ]

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Re: If sides of a quadrilateral X are integers, then is X a square? [#permalink] New post   20 Jun 2021, 04:15
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Re: If sides of a quadrilateral X are integers, then is X a square? [#permalink]
20 Jun 2021, 04:15
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