There is a quadrilateral ABCD with AB=4 cm, BC= 3cm, AD= 2cm, CD= 2cm and angle B=90∘. Can such a quadrilateral exist? Explain. [2 MARKS]
Concept : 1 Mark
Explination : 1 Mark
The above could be a rough sketch of our quadrilateral ABCD. Let us try to understand if
∠ABC=90∘ . By Pythagoras theorem, AC2 = AB2 + BC2
Hence diagonal AC = 5 cm.
Now in triangle ADC, sum of 2 sides has to be greater than 3rd side. But in this triangle AC is greater than AD + DC. Hence the quadrilateral cannot be constructed.