   Chapter A.5, Problem 35E Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Solutions

Chapter
Section Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085
Textbook Problem

In Exercises 35 and 36, use Theorem 2.5.1 to solve the problem. According to this theorem, the number of diagonals in a polygon of n sides is given by D = n ( n − 3 ) 2 Find the number of sides in a polygon that has 9 diagonals

To determine

To find:

To find the number of sides in a polygon that has 9 diagonals.

Explanation

Consider the polygon has 9 diagonals.

Theorem:

If the number of diagonals in a polygon of n sides is given by D=n(n3)2

Where n is number of sides of the polygon.

Given that D=9.

Substitute the value of D=9 in the above equation to get the following,

9=n(n3)2

Then multiply by 2 on both sides of the equation to get the following,

9×2=n(n3)×2218=n(n3)n23n=18

Subtract 18 on both sides to get the following,

n23n18=1818n23n18=0

The general form of the quadratic equation is given below,

ax2+bx+c=0

Where a is the number multiplied by x2, b is the number multiplied by x, and c is the constant term.

The solution for ax2+bx+c=0 when a0 is given below,

x=b±b24ac2a...(1)

Compare the given equation with general equation to get the following,

ax2+bx+c=0n23n18=0

Therefore,

a=1,b=3 and c=18

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