Question

Can we draw a quadrilateral ABCD with following specifications; AB = 3 cm, BC = 5 cm, AD = 4 cm, CD = 7 cm and BD = 8 cm?

• A. With the measure of another diagonal, Yes
• B. Yes definitely
• C. No, it is impossible
• D. With the measure of extra angle, Yes

Answer 1

The correct option is C

No, it is impossible

If we have the measurements of all the sides of a quadrilateral and one of its diagonal, we draw two triangles and hence form a quadrilateral.

ABCD comprises of two triangles $\Delta ADB$ & $\Delta CDB$
In $\Delta ADB$, AB = 3 cm, BD = 8 cm, and AD = 4 cm.
Hence AB + AD < BD
$\Delta ADB$ can't be constructed.
So, quadrilateral ABCD can't be constructed.