Question

In quadrilateral ABCD, AB and DC are parallel, AD and BC are parallel. Find the perimeter of triangle COD if point O is the intersection of diagonals and AC = 20, BD = 20, AB = 13. How do I solve this?

Answer 1

Perimeter = `13 +10+10 = 33`

Explanation:

From the information given we can identify what type of quadrilateral we are given.

The opposite sides are given as parallel, so `ABCD` is at least a parallelogram, which means that the opposite sides are also equal in length, `:.AB = CD = 13`

Draw a diagram and fill in all the information to make it easier.

`AC and BD` are the diagonals as they are given as being equal, we can identify `ABCD` as a rectangle.
The diagonals of a rectangle bisect each other, they share the same midpoint, `O`

`:. AO = OD =DO = OB = 10`

The sides of `Delta COD` are `CD, DO and OC`

The lengths of all these sides known so we can find the perimeter:

`13 +10+10 = 33`