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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