Intermediate Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-894-7
ISBN 13: 978-0-13417-894-3

Chapter 5 - Review Exercises - Page 401: 100

Answer

Length $9$ feet. Width $6$ feet.

Work Step by Step

Let the width of the rectangular sign be $w=x$. Therefore the length of the rectangular sign is $l=x+3$. Area of the rectangular sign is $A=54$ square feet. Formula for the area of the rectangular sign is $A=l\times w$ Plug all values. $54=(x)(x+3)$ Use the distributive property on the right hand side. $54=x^2+3x$ Subtract $54$ from both sides. $54-54=x^2+3x-54$ Simplify. $0=x^2+3x-54$ Rewrite the middle term $3x$ as $9x-6x$. $0=x^2+9x-6x-54$ Group terms. $0=(x^2+9x)+(-6x-54)$ Factor out from each term. $0=x(x+9)-6(x+9)$ Factor out $(x+9)$. $0=(x+9)(x-6)$ Set both factors equal to zero. $x+9=0$ or $x-6=0$ Isolate $x$. $x=-9$ or $x=6$ Take the positive value $x=6$ as $x$ is a dimension. Therefore width $w=6$ feet. Length $l=x+3$ $l=6+3$ $l=9$ feet.
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