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

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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 ( n − 3 ) 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 ( n − 3 ) 2 Then multiply by 2 on both sides of the equation to get the following, 9 × 2 = n ( n − 3 ) × 2 2 18 = n ( n − 3 ) n 2 − 3 n = 18 Subtract 18 on both sides to get the following, n 2 − 3 n − 18 = 18 − 18 n 2 − 3 n − 18 = 0 The general form of the quadratic equation is given below, a x 2 + b x + c = 0 Where a is the number multiplied by x 2 , b is the number multiplied by x , and c is the constant term. Quadratic formula: The solution for a x 2 + b x + c = 0 when a ≠ 0 is given below, x = − b ± b 2 − 4 a c 2 a ... ( 1 ) Compare the given equation with general equation to get the following, a x 2 + b x + c = 0 ⇒ n 2 − 3 n − 18 = 0 Therefore, a = 1 , b = − 3 and c = − 18

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Elementary Geometry for College St...

6th Edition

Daniel C. Alexander + 1 other

Publisher: Cengage Learning

ISBN: 9781285195698

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BuyFind

Elementary Geometry for College St...

6th Edition

Daniel C. Alexander + 1 other

Publisher: Cengage Learning

ISBN: 9781285195698

Solutions

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Answer 3

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Answer 5

To determine

To find:

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

Explanation of Solution

Consider the polygon has 9 diagonals.

Theorem:

If the number of diagonals in a polygon of n sides is given by D=n(n−3)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(n−3)2

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

9×2=n(n−3)×2218=n(n−3)n2−3n=18

Subtract 18 on both sides to get the following,

n2−3n−18=18−18n2−3n−18=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.

Quadratic formula:

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

x=−b±b2−4ac2a...(1)

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

ax2+bx+c=0⇒n2−3n−18=0

Therefore,

a=1,b=−3 and c=−18

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

Elementary Geometry for College St...

Solutions

Elementary Geometry for College St...

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

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