In a parallelogram ABCD O is the intersection point of the diagonals. CD = 15cm, AC = 24cm, DO = 9cm.

| December 2, 2020 | education

In a parallelogram ABCD O is the intersection point of the diagonals. CD = 15cm, AC = 24cm, DO = 9cm. Find the perimeter of triangle AOB.

We know such a wonderful property. In a parallelogram, the intersection point is divided in half. Since AC is a diagonal, it is divided into two (24: 2 = 12) equal segments – AO and CO.
The length of each of these two segments will be 12 cm. We also know the DO segment, whose length is 9 cm. This segment is equal to the BO segment, since the BD diagonal is halved by the intersection point. BO = DO = 9cm. The sides CD and AB are equal between themselves, because we have a parallelogram in front of us, and in a parallelogram the opposite sides are equal. Basically, triangle AOB is equal to triangle COD on three sides. So the perimeter of this triangle will be equal to the perimeter of the CDO triangle.
Paob = Pcod
Paob = AO + BO + BA
AO = CO = 12cm
BO = OD = 9cm
CD = BA = 15cm
Paob = 12 + 9 + 15 = 36cm
Answer: 36cm



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