Question

Can we draw a quadrilateral ABCD with the following data?

AB = 3cm, BC = 5cm, AD = 4cm, CD = 7cm and BD = 8cm

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

Answer 1

The correct option is A

No, it is impossible

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

ABCD comprises of two triangles $△$ ADB &$△$ CDB

In Δ ADB, AB = 3cm, BD = 8cm, and AD = 4cm

AB + AD $<$ BD

Therefore, $△$ ADB can't be constructed.

Therefore​, quadrilateral ABCD can't be constructed