Question

Is it possible to construct quadrilateral $ABCD$ in which $AB=3\text{cm}$ , $BC=4\text{cm}$ , $CD=5.4\text{cm}$ , $DA=5.9\text{cm}$ and diagonal $AC=8\text{cm}$? If not, why?

Answer 1

Given measures are

$AB=3\text{cm},BC=4\text{cm},CD=5.4\text{cm},DA=5.9\text{cm}$ and $AC=8\text{cm}$

Rough diagram:

Here, consider the $△ABC$ within the quadrilateral.

$AB+BC=3+4=7\text{cm}$ and $AC=8\text{cm}$

i.e., the sum of two sides of a triangle is less than the third side, which is absurd.

Hence, we cannot construct such a quadrilateral.