Question

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

• A. No, it is impossible.
• B. With the measure of 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 its one diagonal we draw two triangles and hence, form a quadrilateral

ABCD comprises of two triangles ∆ADB & ∆CDB

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

Hence AB + AD < BD

∆ADB can't be constructed.

So, quadrilateral ABCD can't be constructed.