In a quadrilateral, the diagonals divide it into 4 triangles. It is known that the sum of the perimeters

| June 26, 2021 | education

In a quadrilateral, the diagonals divide it into 4 triangles. It is known that the sum of the perimeters of these triangles is 73cm, and the perimeter of the quadrilateral is 29cm. What is the sum of the lengths of the diagonals?

1. Each side of the quadrilateral belongs to one of the resulting triangles, which means that in the sum of the perimeters of the indicated triangles, the perimeter of the quadrilateral is also taken into account.

2. Each of the parts of both diagonals belongs to the side of the two resulting triangles, which means that it is counted twice in the sum of the perimeters of these triangles, that is, the diagonals are counted twice there.

Let’s calculate what the sum of the diagonals is equal to for the following values:

(73 – 29): 2 = 22.

Answer: 22 centimeters.



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