in a rhombus ABCD , AB = 13 cm and AC = 24 cm. find BD

Dear Student, 
In a rhombus we know that diagonal bisect and are perpendicular so 

$$\begin{gathered} \mathrm{AE} = \mathrm{EC} = 12 \mathrm{and} \\ \mathrm{hence} \mathrm{in} \mathrm{triangle} \mathrm{AEB}, \\ \mathrm{BE}\hspace{0.17em}= \sqrt{{13}^2-{12}^2} \mathrm{as} \mathrm{AB} \mathrm{is} \mathrm{hypotenuse} \\ = 5 \\ \mathrm{So} \mathrm{BD} = 2\mathrm{BE}\hspace{0.17em}= 2\times 5 = 10 \mathrm{cm} \\ \mathrm{Regards} \end{gathered}$$