Elementary Geometry for College Students (5th Edition)

Published by Brooks Cole
ISBN 10: 1439047901
ISBN 13: 978-1-43904-790-3

Appendix A - A.4 - Quadratic Equations - Exercises - Page 561: 36

Answer

$n = 5$ sides.

Work Step by Step

$D = \frac{n(n-3)}{2}$ $n = \frac{n(n-3)}{2}$ $2n = n(n-3)$ $2n = n^{2} - 3n$ $n^{2} - 3n = 2n$ $n^{2} - 3n -2n= 0$ $n^{2} - 5n = 0$ $n(n-5) = 0$ $n = 0, 5$ A polygon cannot have $0$ sides, so therefore $n = 5$ sides.
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