Elementary Algebra

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

Chapter 3 - Equations and Problem Solving - 3.5 - Problem Solving - Problem Set 3.5: 14

Answer

The length of the side of the square is 6 inches. The width of the rectangle is 3 inches. The length of the rectangle is 9 inches.

Work Step by Step

Let X represent the side of the square. The width of the rectangle is 9 inches less than twice the side of the square. This equals 2X - 9. The length of the rectangle is 3 inches less than twice the 2 side of the square. This equals 2X - 3. The perimeter of the square is 4 $\times$ X = 4X. The formula for the perimeter of the rectangle is width + width + length + length. The perimeter of the rectangle is: P = 2X - 9 + 2X - 9 + 2X - 3 + 2X - 3 = 8X - 24. Since their perimeters are equal, we can set up the following equation: 4X = 8X - 24 24 = 4X Divide both sides by 4. X = 6 The length of the side of the square is 6. The width of the rectangle is 2X - 9 = 2 $\times$ 6 - 9 = 3. The length of the rectangle is 2X - 3 = 2 $\times$ 6 - 3 = 9.
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