The perimeter of parallelogram ABCD is equal to 10 cm. Find the length of diagonal BD if you know that the perimeter of △ABD is 8 cm.

see the attached figure

Let
P1-------------> Perimeter of parallelogram ABCD
P2-------------> Perimeter of △ABD

we know that
P1=10 cm
P1=2*(AD)+2*(AB)=10------------> AB+AD=5-----------> equation 1
and
P2=AD+AB+DB
P2=8 cm------------>AD+AB+DB=8-------- AB+AD=8-DB-----> equation 2
I substitute 1 in 2

(5)=8-DB----------> DB=8-5-----------> DB=3 cm

the answer is DB=3 cm