Construct, if possible, a quadrilateral ABCD in which AB = 6cm, B… - Vidyadip

Question

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

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Answer

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 = 8.5cm
and AC = 11cm. i.e., AD + CD < AC, which is not possible.
So, the construction is not possible.

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