The perimeter of parallelogram ABCD is 50 cm, find its diagonal if the perimeter of triangle ABD is 40 cm.

The perimeter of a parallelogram is equal to the sum of its four sides. In a parallelogram, the opposite sides are parallel and equal.

P = AB + BC + CD + AC;

AB = CD; AD = DC;

PABCD = 2 (AB + AD) – knowing the perimeter, we find the sum of the lengths of the two sides of the parallelogram;

AB + AD = PABCD: 2;

AB + AD = 50: 2 = 25 (cm).

The perimeter of a triangle is equal to the sum of its three sides.

PABD = AB + AD + BD – knowing the perimeter of the triangle and the sum of its two sides AB and AD, we find the length of the side BD, which is the diagonal of the parallelogram;

BD = PABD – (AB + AD);

BD = 40 – 25 = 15 (cm).

Answer. 15 cm.