Construct, if possible, a quadrilateral ABCD in which AB = 6 cm, BC = 7 cm, CD = 3 cm,


Construct, if possible, a quadrilateral ABCD in which AB = 6 cm, BC = 7 cm, CD = 3 cm, AD = 5.5 cm and AC = 11 cm. Give reasons for not being able to construct, if you cannot. (Not possible, because in triangle ACDAD + CD < AC).


Such a quadrilateral cannot be constructed because in a triangle, the sum of the length of its two sides must be greater than the that of the third side

But here in triangle ACD,

AD + CD = 5.5 + 3 = 8.5 cm

and AC = 11 cm

i.e., AD + CD <  AC, which is not possible.

So, the construction is not possible.

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