College Algebra 7th Edition

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

Chapter 2, Functions - Focus on Modeling - Modeling with Functions - Problems - Page 277: 15

Answer

$b\sqrt{4-b}$ where $0\lt b\lt 4$.

Work Step by Step

Let the other two sides have length $x$. Then we also know that $2x+b=8$ because the perimeter is $8$. Thus, we can solve for $x$: $x=(8-b)/2$. Then the area of the triangle can be calculated with Heron's formula: $A=\sqrt{s(s-a)(s-b)(s-c)}=\sqrt{4(4-(8-b)/2)(4-b)(4-(8-b)/2)}=\sqrt{4(b/2)(4-b)(b/2)}=b\sqrt{4-b}$ and $0\lt b\lt 4$. Where $s=(a+b+c)/2=8/2=4$.
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