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?

Answer 1

No,
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 not possible.

In a triangle, the sum of two sides of a triangle should be greater than the third side.

Hence, we cannot construct such a quadrilateral.