# 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 = $13 + 10 + 10 = 33$

#### Explanation:

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

The opposite sides are given as parallel, so $A B C D$ is at least a parallelogram, which means that the opposite sides are also equal in length, $\therefore A B = C D = 13$

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

$A C \mathmr{and} B D$ are the diagonals as they are given as being equal, we can identify $A B C D$ as a rectangle.
The diagonals of a rectangle bisect each other, they share the same midpoint, $O$

$\therefore A O = O D = D O = O B = 10$

The sides of $\Delta C O D$ are $C D , D O \mathmr{and} O C$

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

$13 + 10 + 10 = 33$

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