Common Mistakes in Geometry Questions - Exercise Question #1

Note: This questions is related to the article on Common Errors in Geometry

Kindly go through the article once, before solving the question or going through the solution.


Official Solution


Given: ABCD is a quadrilateral.


Analysing statement 1:

The first statements states :

The diagonals bisect each other at \(90^o\) and they are equal.


From the above statement, we can conclude that the quadrilateral is a square.

But to find the area of the quadrilateral we need the length of each side, which is not given.

Hence statement 1 is not sufficient to answer the question.


Analysing statement 2:

The length of each diagonal is 10 cm.

Using only the 2nd statement, we cannot find the area of the quadrilateral, since we don't know what kind of quadrilateral it is.

Hence statement 2 is not sufficient to answer the question.


Combining statement 1 and 2:


Using both the statements, we can conclude that the quadrilateral is a square and the length of it's diagonal is 10cm.

Therefore, AB = BC = CD = AD

AC = BD = 10 (diagonals)



Since ABCD is a square angle ABC = 9\(0^o\), therefore we can infer that the diagonal(AC) is the hypotenuse and the sides AB and BC are the perpendicular and base.

Hence we can write A\(B^2\) + B\(C^2\) = A\(C^2\)

2A\(B^2\) = 1\(0^2\).............(i)

And we know the area of the square = (side\()^2\) = A\(B^2\)

We can find the value of AB from (i) and hence we can find the area of the square!


Hence combining both the statements we can find out the answer.


Correct Option : C


Thanks,
Saquib
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e-GMAT