IIITH-PGEE 2017

Question

Let X be a length used to make three sides of a rectangle. Area of rectangle will be:

A. $X^{2}/9$

B. $(X-a)^{2}/4$

C. $(X+a)^{2}/16$

D. None of the above

Comments

@warlock lord

Option A is only for distraction if nothing mentioned how can u divide X into 3 equal part.

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Because square is a rectangle too. And conceptually it is not wrong to consider all sides same and still call it a rectangle. And hence "None of these" can be a trick too.

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Many questions were ambiguous last year. Hope it doesn't happen this time.

Answer 1

I feel Option A is correct

We know from properties that square is a type of rectangle with all sides measuring equal in length

So, let us consider length of sides of rectangle = $a$

Now , in the given question, the length of 3 sides of rectangle is given  = X

So we can rewrite it as , $X = 3a$

Now squaring on both sides , we get  

$X^{^{2}} = 9a^{2}$

ie , $X^{^{2}}/9 = a^{2}$ ,

So , we know that area of square (We assume it as an equal side rectangle) =  $a^{2}$

So the answer is Opt (A) = $X^{2}/9$

Comments

how can you assume it as a square? This is not right way to do it. Here 2 sides definitely will be same but how you can say that all side will be equal. 

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Actually, all rectangles need not have a pair of equal sides, we need to use our imagination. 

According to properties, if a rectangle has equal sides then it is said to be a square, hope you agree with this point, below I have attached the exact information from Wikipedia.

" In Euclidean plane geometry, a rectangle is a quadrilateral with four right angles. It can also be defined as an equiangular quadrilateral, since equiangular means that all of its angles are equal (360°/4 = 90°). It can also be defined as a parallelogram containing a right angle. A rectangle with four sides of equal length is a square. The term oblong is occasionally used to refer to a non-square rectangle.^[1][2][3] A rectangle with vertices ABCD would be denoted as  ABCD." 

You can see on the 3rd line 

So, they have not mentioned that the only pair of sides is equal, so we consider the given rectangle to be a square. 

 So, that's why I feel my answer is correct and not telling that my answer is only correct :-).

Even your analogy is correct. 

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yes, I know that square is also a rectangle.but my question still same.why are you assuming all sides equally? you can't assume anything only to match options.in my opinion either something wrong in this question or answer will be none of these.

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I think to a certain extinct your argument is correct

Yeah , I feel there may be some missing information or some mistake :-)