Elementary Algebra

Published by Cengage Learning
ISBN 10: 1285194055
ISBN 13: 978-1-28519-405-9

Chapter 6 - Factoring, Solving Equations, and Problem Solving - 6.3 - Factoring Trinomials of the Form x^2+bx+x - Problem Set 6.3: 60

Answer

The square is 4 by 4, and the rectangle is 6 by 8.

Work Step by Step

Let s be the side of the square. Thus: $ s^2 + lw =64$ Since l =s+4 and w = s+2, we find: $ s^2 + (s+2)(s+4) = 64 \\ 2s^2 + 6s +-56 = 0 \\ 2(s-4)(s+7)=0$ Since s cannot be negative, we find: $ s=4 $ Thus, the square is 4 by 4, and the rectangle is 4+2 by 4+4, which is 6 by 8.
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