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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

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ConceptConstructing a Quadrilateral When Two Adjacent Sides and Three Angles Are Known

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?

APPEARS IN

 RD Sharma Solution for Mathematics for Class 8 by R D Sharma (2019-2020 Session) (2017 to Current)
Chapter 18: Practical Geometry (Constructions)
Ex. 18.1 | Q: 8 | Page no. 4
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.
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