#### 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).

#### Solution

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.

Is there an error in this question or solution?

Solution 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, Concept: Constructing a Quadrilateral - When Two Adjacent Sides and Three Angles Are Known.