Elementary Geometry for College Students (7th Edition)

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

Appendix A - A.5 - The Quadratic Formula and Square Root Properties - Exercises - Page 562: 36


The number of sides in the polygon is $~5$

Work Step by Step

We can solve the equation as follows: $\frac{n~(n-3)}{2} = D$ $\frac{n~(n-3)}{2} = n$ $n~(n-3) = 2n$ $n^2-3n = 2n$ $n^2-5n = 0$ $n~(n-5) = 0$ $n=0~~$or $~~n-5=0$ $n = 0~~$ or $~~n=5$ Since the number $n$ must be a positive number, $n=5$ The number of sides in the polygon is $~5$
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