Elementary Geometry for College Students (7th Edition) Clone

Published by Cengage
ISBN 10: 978-1-337-61408-5
ISBN 13: 978-1-33761-408-5

Chapter 4 - Review Exercises - Page 217: 15

Answer

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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