Question

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

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

Answer 1

The correct option is A

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.