The perimeter of parallelogram ABCD is 10 cm.Find the length of the diagonal BD,

The perimeter of parallelogram ABCD is 10 cm.Find the length of the diagonal BD, knowing that the perimeter of triangle ABD is 8 cm

A parallelogram is a quadrangle in which opposite sides are parallel and equal to each other:

AB = CD;

BC = AD.

Since the perimeter of a parallelogram is the sum of all its sides:

RAVSD = AB + BC + CD + AD, then:

(AB + AD) = PABCD – (BC + CD).

Since in a parallelogram the opposite sides are equal, then:

(AB + AD) = (BC + CD);

(AB + AD) = (BC + CD) = PABCD / 2;

(AB + AD) = (BC + CD) = 10/2 = 5 cm.

Since the perimeter of the triangle ΔABD is 8 cm, the sum of the sides AB and AD is 5 cm, then:

BD = PABD – (AB + AD);

ВD = 8 – 5 = 3 cm.

Answer: the length of the diagonal BD is 3 cm.