Question

For a quadrilateral PQRS where PQ = $4$ cm, QR = $6$ cm, RS = $5$ cm and PS = $5.5$ cm, the value of PR should be less than ____ cm.

___

Answer 1

Quadrilateral PQRS can be considered as the combination of $2$ triangles PQR and PSR.

One side of a triangle cannot be greater than the sum of other $2$ sides.

Therefore, PR $<$ PQ + QR

PR $<4+6=10$ ....... (1)

PR $<$ PS + SR

PR $<5.5+5=10.5$......... (2)

From (1) and (2), it implies that PR $<10$ cm