Question

Is it possible to construct a quadrilateral ABCD in which AB = 3 cm, BC = 4 cm, CD = 5.4 cm, DA = 5.9 cm and diagonal AC = 8 cm? If not, why? [2 marks]

Answer 1

No, we cannot construct the quadrilateral.

(0.5 mark)

Given measures are AB = 3 cm, BC = 4 cm, CD = 5.4 cm,
DA = 5.9 cm and AC = 8 cm
Here, we observe that AB + BC = 3 + 4 = 7 cm and AC = 8 cm
i.e. the sum of two sides of a triangle is less than the third side, which is absurd.

(1.5 mark)

Hence, we cannot construct such a quadrilateral.