The perimeter of the triangle ABD is 12cm, the perimeter of the triangle BDC is 30cm, and the perimeter

The perimeter of the triangle ABD is 12cm, the perimeter of the triangle BDC is 30cm, and the perimeter of the quadrilateral ABCD is 32cm. Determine the length of the line segment BD.

To solve the problem, you must remember that the perimeter of any figure is equal to the sum of all its sides.

In this case, the perimeter of triangle ABD is:

P (ABD) = AB + BD + AD = 12 cm;

perimeter of triangle BDC:

P (BDC) = BD + DC + BC = 30 cm;

perimeter of quadrilateral ABCD:

P (ABCD) = AB + BC + CD + AD = 32 cm.

Thus,

P (ABCD) – P (ABD) + P (BDC) = 2 (DC + BC) = 32 – 12 + 30 = 50,

whence DC + BC = 25 cm.

As a result, Р (ВDC) – DC + ВС = ВD = 30 – 25 = 5 cm.

Answer: the length of the segment BD is 5 cm.