State true or false: A quadrilateral ABCD can be constructed, such that AB = 3 cm, BC = 4 cm, CD = 5.4 cm, DA = 5.9 cm and diagonal AC = 8 cm.

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True

False

answer is B.

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Detailed Solution

Here, we have, to check if the quadrilateral with the side dimensions as AB = 3cm, BC = 4 cm, CD = 5.4cm,
DA = 5.9cm and its diagonal AC = 8cm.
So, let's verify if the dimensions are correct or not.
So, let us consider the triangle formed by the sides AB, BC and the diagonal AC.
Now, for a triangle to be constructed, the sum of its two sides must be more than the length of the third side as per the triangle inequality theorem.
So, we will check if this triangle within the quadrilateral is possible or not and accordingly decide if the quadrilateral can be constructed or not.
So, as per the triangle inequality theorem,
AB + BC > AC
Substituting the lengths as mentioned, we get,
3 + 4 > 8
7 > 8
This is not possible.
So, as the triangle within the quadrilateral formed by the two sides AB and BC and a diagonal AC cannot be constructed so is the quadrilateral.
Hence, the given statement is false.
Hence, the correct option is (2).

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