sana.noor wrote: the answer is C but i guess it should be B because we know that in rectangle the diagonals arnt perpendicular to each other.

A rectangle is a quadrilateral (4-sided figure) with 4 right angles.
Given this definition, a square is a type of rectangle. In a square, the diagonals are perpendicular to each other. So, statement 2 does not rule out the possibility that the quadrilateral is a rectangle.

Cheers,
Brent

sana.noor wrote:Is the quadrilateral a rectangle ?

1) Two of the sides measure 6 long and 2 of them measure 8 long.

2) The diagonals are perpendicular to each other.

Target question: Is the quadrilateral a rectangle?

Statement 1: Two of the sides measure 6 long and 2 of them measure 8 long.
The two quadrilaterals below both satisfy the condition in statement 1.

So, the quadrilateral could be a rectangle, or the quadrilateral might not be a rectangle
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: The diagonals are perpendicular to each other.
The two quadrilaterals below both satisfy the condition in statement 2.

IMPORTANT: As I mentioned in my earlier post, a square is a type of rectangle.
So, the quadrilateral could be a rectangle, or the quadrilateral might not be a rectangle
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined:
Consider statement 2 first. If the diagonals are perpendicular to each other, then the quadrilateral could be a rectangle AS LONG AS THAT RECTANGLE IS A SQUARE.
Then, when we consider statement 1 (two sides of length 6 and two sides of length 8), we see that we cannot have a square.
So, from this, we can be certain that the quadrilateral is not be a rectangle
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

By the way, the shape looks something like this:


Answer = C

Cheers,
Brent