Question

A student wants to construct a quadrilateral ABCD with the measurements AB = 3cm, BC = 4cm, CD = 4.5cm, AD = 2cm and BD = 6cm but he could not construct it .What could be the reason?

• A. A quadrilateral cannot be constructed if the measurements of four sides and a diagonal is given
• B. Length of a diagonal can not be less than the length of the sides of the quadrilateral
• C. In ΔBCD, sum of the sides BC and CD is greater than the third side BD
• D. In ΔABD, sum of sides AB and AD is less than the third side BD

Answer 1

The correct option is A

A quadrilateral cannot be constructed if the measurements of four sides and a diagonal is given

In a triangle, sum of the length of any two sides should always be greater than the length of the third side. Here, Sum of sides AB and AD is less than the third side BD of triangle ABD. Hence, the quadrilateral cannot be constructed.