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

Question

(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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IanStewart · Answer

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.

bM22 · Answer

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.

vipulshahi · Answer

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

HoneyLemon · Answer

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

sambitspm · Answer

Kindly see the attachment.
Both are insufficient.
E

bumpbot · Answer

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

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