The diagonals of the parallelogram ABCD are 5 cm and 7 cm, the side of the BC is 4 cm.

The diagonals of the parallelogram ABCD are 5 cm and 7 cm, the side of the BC is 4 cm. Find the perimeter of the ADK triangle where K is the intersection point of the diagonals.

The solution of the problem:

Side AD = BC = 4 cm.

The diagonals of the parallelogram are halved at the intersection.

AK = KС = AC / 2;

AK = 7/2 = 3.5 cm.

ВK = KD = BD / 2;

ВK = 5/2 = 2.5 cm.

Let’s define the perimeter P of the triangle AKD.

P = AD + AK + KD;

P = 4 + 3.5 + 2.5 = 10 cm.

Answer: The perimeter of triangle AKD is 10 cm.