Question

There is a quadrilateral ABCD with AB=4 cm, BC= 3cm, AD= 2cm, CD= 2cm and angle $B={90}^{\circ }$. Can such a quadrilateral exist? Explain.

Answer 1

The above could be a rough sketch of our quadrilateral ABCD. Let us try to understand if

$\angle ABC={90}^{\circ }$ . By Pythagoras theorem, ${AC}^2$ = ${AB}^2$ + ${BC}^2$

Hence diagonal AC = 5 cm.

Now in triangle ADC, sum of 2 sides has to be greater than 3^rd side. But in this triangle AC is greater than AD + DC. Hence the quadrilateral cannot be constructed.