DS2522

Question

please solve this. 

Is it the rectangular ?

thank you

Dookie · Answer

In a rectangle, diagonals are equal.
Using both statements you can say that this is a Rectangle. 
In fact, i think that even the first statement by itself is enough.
But we are requested to calculate the area, and the information given is insufficient. 

So i pick E.

ian7777 · Answer

I go for E, also. Same explanation as Dookie.

chunjuwu · Answer

Hello, Dookie. 

If we set the intersection of the two diagonal lines O
, then the triangle ORQ is an isosceles triangle. 

And, if the angle ROQ equals 90 degree, we can decide the area of region PQRS. 

But the fact that the angle ROQ equals 90 degree is the definition of a square rather than a rectangle. So, we cannot decide it. 

Am I right ? thank you

ian7777 · Answer

chunjuwu, you are right about that. There is nothing here which tells us that the angle of the intersection is 90. If so, it would be a square, and we would know the area. Remember, a square is a rectangle, just a more specific one, and it is certainly a quadrilateral. So that would have been fine, but we can't just decide the angle of the middle, and it can't be detirmined from the problem.

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