Discussion
Which of the following quadrilateral ABCD cannot be constructed ?
Answer: C
The quadrilateral that cannot be constructed is AB = 3, BC = 5, AC = 6, AD = 3, CD = 2.
The diagonal AC splits the quadrilateral into triangles ABC and ADC, and each must satisfy the triangle inequality. In this option, triangle ADC has sides 3, 2 and 6, but 3 + 2 = 5 is less than 6, so the triangle, and hence the quadrilateral, cannot be drawn.
In every other option both triangles are possible: 3, 5, 4 with 6, 6, 4; 2, 4, 4 with 5, 5, 4; and 3, 5, 6 with 3, 5, 6.
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