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: 89

Answer

The length of a side of the square is $\frac{4}{\pi}$ units.

Work Step by Step

Let $A = $ area of the circle Let $x = $ length of a side of a square Let $r = $ radius of the circle $A = \pi r^{2}$ $4x = A$ $r = x$ $4x = \pi r^{2}$ $4x = \pi x^{2}$ $4x - \pi x^{2} = 0$ $x(4-\pi x) = 0$ We find set the factors equal to zero: $x=0$ $4 - \pi x = 0$ $-\pi x = -4$ $\pi x = 4$ $x = \frac{4}{\pi}$ $x = 0, \frac{4}{\pi}$ We do not consider x=0, for a length of a a side cannot equal 0. The length of a side of the square is $\frac{4}{\pi}$ units.
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