Elementary Algebra

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

Chapter 6 - Factoring, Solving Equations, and Problem Solving - 6.1 - Factoring by Using the Distributive Property - Problem Set 6.1: 91

Answer

The dimensions of the square is $3 \times 3$ inches. The dimensions of the rectangle is $6 \times 3$ inches.

Work Step by Step

Let $a = $ area of the rectangle Let $x = $ area of the square Let $p = $ width of rectangle and length of square $a = 2x$ $2x = 2p^{2}$ $a = 6 \times p$ $a = 2p^{2}$ $6p = 2p^{2}$ $6p - 2p^{2}= 0$ $2p(3 - p) = 0$ $p = 0, 3$ Recall, 0 is not a valid value for length. Therefore, the dimensions of the square are $3 \times 3$ inches. Therefore, the dimensions of the rectangle are $6 \times 3$ inches.
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