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, - Mathematics

Answer in Brief

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).

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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.

Concept: Constructing a Quadrilateral When Two Adjacent Sides and Three Angles Are Known

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Chapter 18: Practical Geometry (Constructions) - Exercise 18.1 [Page 4]

Q 8 Q 7 Q 1

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