Elementary Geometry for College Students (6th Edition)

Published by Brooks Cole

Appendix A - A.5 - The Quadratic Formula and Square Root Properties - Exercises - Page 555: 33

Answer

The width is $5$ The length is $8$

Work Step by Step

Let's consider a trinomial in this form: $~x^2+bx+c$ To factor this trinomial, we need to find two numbers $r$ and $s$ such that $r+s = b$ and $r\times s = c$ Then the next step is to rewrite the trinomial as follows: $~x^2+bx+c = (x+r)~(x+s)$ We can rewrite the given equation: $x~(x+3) = 40$ $x^2+3x = 40$ $x^2+3x-40 = 0$ To factor the left side of this equation, we need to find two numbers $r$ and $s$ such that $r+s = 3~$ and $~r\times s = -40$. We can see that $(8)+(-5) = 3~$ and $(8)\times (-5) = -40$ We can solve the equation as follows: $x~(x+3) = 40$ $x^2+3x = 40$ $x^2+3x-40 = 0$ $(x+8)~(x-5) = 0$ $x+8=0~~$or $~~x-5=0$ $x = -8~~$ or $~~x=5$ Since the width must be a positive number, the width is $5$ Then the length is $5+3$ which is $8$

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