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: 15

Answer

The length of the radius of the circle is 7 cm.

Work Step by Step

Let X represent the length of the radius of the circle. The length of the side of the square is X, too, because it is equal to the radius of the circle. The perimeter of the square equals 4 $\times$ X = 4X. The circumference of the circle is 2 $\times$ $\pi$ $\times$ radius = 2 $\times$ $\pi$ $\times$ X. Since the circumference of the circle is 15.96 centimeters longer than the perimeter of the square, we can set up the following equation: 2 $\times$ $\pi$ $\times$ X = 4X + 15.96 $\pi$ is about 3.14, so we can plug its value in the equation. 2 $\times$ 3.14 $\times$ X = 4X + 15.96 6.28X = 4X + 15.96 Subtract 4X from both sides. 2.28X = 15.96 Divide both sides by 2.28 X = 7 The length of the radius of the circle is 7 cm.
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