Question

In a quadrilateral ABCD, AB = 7 cm, BC = 5 cm, AC = 9 cm, AD = 6 cm, CD = 2 cm. Which of the following options is true about the construction of a quadrilateral ABCD?

• A. It is possible to draw the quadrilateral
• B. It is not possible to draw the quadrilateral since AD + DC < AC
• C. It is possible to draw the quadrilateral since AD + DC < AC
• D. None of these

Answer 1

The correct option is B It is not possible to draw the quadrilateral since AD + DC < AC

In a triangle, sum of any two sides should be greater than the third side. A quadrilateral is made up of two triangles.

It is given that AD = 6 cm, CD =2 cm and AC = 9 cm. AC $>$ AD + CD. This does not satisfy triangle inequality and hence the quadrilateral ABCD cannot be drawn.