College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter 1, Equations and Graphs - Section 1.4 - Solving Quadratic Equations - 1.4 Exercises - Page 124: 77

Answer

width: $120~ft$ length: $126~ft$

Work Step by Step

Let $x$ be the width. Then the length is $x+6$. Thus, by the Pythagorean Theorem: $x^2+(x+6)^2=174^2\\x^2+x^2+12x+36=30276\\2x^2+12x=30240\\x^2+6x-15120=0\\(x-120)(x+126)=0$ Hence, $x=120$ or $x=-126$. However, the dimensions must be positive, so we throw out the negative solution. Thus, the width is $x=120$ and the length is $126$.
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