# The diagonals of rectangle ABCD intersect at point O. The perimeter of triangle ACD is 30 cm and the perimeter

March 24, 2021 | education

| **The diagonals of rectangle ABCD intersect at point O. The perimeter of triangle ACD is 30 cm and the perimeter of triangle AOD is 18 cm.Find the perimeter of triangle COD if the diagonal of the rectangle is 13 cm.**

The solution of the problem:

AO = OC = AC: 2 = 13: 2 = 6.5 cm.

BO = OD = BD: 2 = 13: 2 = 6.5 cm.

Perimeter of a triangle AOD = AO + OD + AD;

18 = 6.5 + 6.5 + AD;

AD = 18 – (6.5 + 6.5);

AD = 18 – 13 = 5 cm.

Perimeter of the triangle ACD = AC + AD + CD;

30 = 13 + 5 + CD;

CD = 30 – (13 + 5);

CD = 30-18;

СD = 12 cm.

Let’s define the perimeter (P) of the triangle COD.

P = CO + OD + CD;

P = 6.5 + 6.5 + 12;

P = 25 cm.

Answer: The perimeter of the COD triangle is 25 cm.

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