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

Question

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 $ACD, AD + CD < AC).$

✓

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 $ACD. AD + CD = 5.5 + 3 = 8.5\ cm$ and $AC = 11\ cm.$
i.e., $AD + CD < AC,$ which is not possible. So, the construction is not possible.

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