In the figure , a circle touches all the four sides of a quadrilateral ABCD whose sides AB = 6.5 cm, BC = 5.4 cm and CD = 5.3 cm. The length of AD is :

4.6 cm 6.4 cm 5.8 cm 6.2 cm

6.4 cm

We have, AB = 6.5 cm,  BC = 5.4 cm,  CD = 5.3 cm We know that, AP = AS, BP = BQ, CR = CQ, DR = DS = (AP + PB) + (DR + RC) = (BQ + QC) + (AS + DS) = AB + CD = AD + BC = 6.5 + 5.3 = AD + 5.4 = 11.8 = AD + 5.4 = AD = 11.8 - 5.4  = 6.4 cm