In a quadrilateral abcd, ab || dc and ad || bc. find the perimeter of triangle cod if the diagonals of the quadrilateral intersect each other at point o and ac = 20in, bd = 20in, ab = 13in.

Draw a diagram as shown below.

The diagonals are equal in length. Because AB || DC and AD || BC, the quadrilateral is a square.

Because the diagonals bisect each other at O, therefore
DO = BO = 10.
Likewise,
AO = CO = 10

Because AB = 13, therefore DC = 13.
The perimeter of ΔCOD is CO + CD + DO = 10 + 13 + 10 = 33 in

33 in

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