We have,

ABCD is a rhombus

AC and BD are the diagonals with length 10cm and 24 cm respectively.

We know that rhombus of diagonal bisects each other at 90

∴ AO=OC=5cm and BO=OD=12cm

In AOB

AB²=AO²+BO²

AB²=5²+12²

AB²=25+144

AB²=169

AB=

AB=13 cm