# In the rhombus ABCD, the diagonals intersect at point O. The perimeter of the triangle AOD

In the rhombus ABCD, the diagonals intersect at point O. The perimeter of the triangle AOD = 14 cm and the perimeter of the triangle ACD = 20 cm, find BD.

We denote the length of the segment BD = X,

Then the length of the segment OD = X / 2.

Since the perimeter (P) of any figure is equal to the sum of its sides, and the triangle AOD is half of the isosceles triangle ACD, then:

PAOD – X / 2 = P ACD / 2;

X = 2 * (PAOD – P ACD / 2) = 2 * (14 – 20/2) = 2 * (14 – 10) = 2 * 4 = 8 cm.

Answer: segment BD = 8 cm.

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