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?

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Feb 25, 2018


Perimeter = #13 +10+10 = 33#


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#

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