The diagonal of the parallelogram, equal to 10 cm, divides it into two equal triangles with perimeters equal

The diagonal of the parallelogram, equal to 10 cm, divides it into two equal triangles with perimeters equal to 36 cm. Find the perimeter of the parallelogram.

By condition, the perimeter of triangle ABC is equal to the perimeter of triangle ACD.

Ravs = AB + BC + AC = 36 cm.

Dist = AD + CD + AC = 36 cm.

Let’s add the perimeters of the triangles.

Ravs + Rasd = AB + BC + AC + AD + CD + AC = 72 cm.

Let us group the terms.

72 = (AB + BC + CD + AD) + (AC + AC).

In the first brackets is the perimeter of the parallelogram, in the second is the sum of the two diagonals.

Then Ravsd = 72 – 2 * AC = 72 – 20 = 52 cm.

Answer: The perimeter of the parallelogram is 52 cm.