# Chapter 4 - Review Exercises - Page 217: 15

52

#### Work Step by Step

For parallelogram ABCD to have perpendicular diagonals, then parallelogram ABCD is actually a rhombus. Since ABCD is a rhombus, then the diagonals also bisect each other. This will create four congruent right triangles inside rhombus ABCD with leg lengths of 5 and 12. In a right triangle, if the leg lengths are 5 and 12, then the hypotenuse is 13. The hypotenuse of each right triangle is a side of rhombus ABCD. Thus, each side has lenght 13. $13\times4=52$

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