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Common Errors in GeometryKindly go through the article once, before solving the question or going through the solution.
Official SolutionGiven: 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 : CThanks,
Saquib
Quant Expert
e-GMAT In statement 2, it is stated that the length of each diagonal is 10 cm. This implies that both the diagonals are equal in length. I was under the impression that square is the only quadrilateral that has both diagonals equal in length. Or is there any other quadrilateral that has it's diagonals equal ?