The diagonals of parallelogram ABCD equal 5 cm and 11 cm, intersect at point O. Find the perimeter

| August 10, 2021 | education

The diagonals of parallelogram ABCD equal 5 cm and 11 cm, intersect at point O. Find the perimeter of triangle BCO if AD 7 cm.

1) First of all, we write down the formula by which we find the perimeter P of the triangle BCO.
The perimeter is the sum of all the sides of the shape.
Based on this, we will write.
P = BC + OC + OB.
2) By condition AD = 7cm.
Since the parallelogram is given by the condition ABCD, then BC = AD = 7 (cm).
3) Now let’s find the OC side.
Pay attention: one of the properties of the parallelogram diagonals is that these diagonals are halved by the intersection point.
It follows from this that the diagonal AC = AO + OC.
Since AO = OC, then we write AC = 2OC.
Now let’s express and calculate OC.
OC = AC: 2.
OC = 11: 2.
OC = 5.5 (cm).
4) Using the same property of the parallelogram, we express and calculate the OB side.
BD = OB + OD.
Since the diagonal BD is halved by the intersection point O, we write OB = OD.
BD = 2OB.
OB = BD: 2.
OB = 5: 2.
OB = 2.5 (cm).
5) Find the perimeter of the BCO.
P = 7 + 5.5 + 2.5.
P = 15 (cm).
Answer: 15 cm is the perimeter of the triangle BCO.



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