Algebra 1: Common Core (15th Edition)

Published by Prentice Hall
ISBN 10: 0133281140
ISBN 13: 978-0-13328-114-9

Chapter 9 - Quadratic Functions and Equations - 9-3 Solving Quadratic Equations - Practice and Problem-Solving Exercises - Page 564: 34

Answer

Quadratic equation $\pi r^2=90$. r=$5.4\;cm$.

Work Step by Step

Let the radius of the circle be $=r$. Area of the circle $=\pi r^2$. Given area of the circle $=90\;cm^2$. Equate both areas. $\Rightarrow \pi r^2=90$ Divide both sides by $\pi$. $\Rightarrow \frac{\pi r^2}{\pi}=\frac{90}{\pi}$ Simplify. $\Rightarrow r^2=\frac{90}{\pi}$ Take the square root on both sides. $\Rightarrow \sqrt{ r^2}=\pm\sqrt{\frac{90}{\pi}}$ Simplify. $\Rightarrow r=\pm5.4\;$ The area cannot have a negative sign. Hence, the radius of the circle is $5.4\;cm$.
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