Can we draw a quadrilateral ABCD with following measurements: AB = 3cm, BC = 5cm, AD = 4cm, CD = 7cm and BD = 8cm?
No, it is impossible
If we have the measures of all the sides of a quadrilateral and its one diagonal, we can draw two triangles and hence, form a quadrilateral.
ABCD comprises of two triangle △ ADB &△ CDB
In Δ ADB, AB = 3cm, BD = 8cm, and AD = 4cm
Since, AB + AD < BD
△ ADB can't be constructed.
So, quadrilateral ABCD can't be constructed.