The perimeter of the triangle ABC is 12 cm, the perimeter of the triangle BDC is 30 cm

The perimeter of the triangle ABC is 12 cm, the perimeter of the triangle BDC is 30 cm, and the perimeter of the quadrangle ABCD is 32 cm. Determine the length of the segment BD.

Given:
P ABC = 12 cm
P BDC = 30cm
P ABDC = 32 cm

Find:
BD -?

Solution:
Let us express BC.
BC = 12 – (BA + AC)
BC = 30 – (CD + DB)
Now we express the brackets.
(BA + AC) = 12 – BC
(CD + DB) = 30 – BC.
P ABCD = BA + AC + CD = DB
Now we plug in the data and solve the resulting equation.
12 – BC + 30 – BC = 32
42 – 2BC = 32
42 – 32 = 2BC
10 = 2BC
BC = 5