Introductory Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-805-X
ISBN 13: 978-0-13417-805-9

Chapter 8 - Section 8.3 - Operations with Radicals - Exercise Set: 89

Answer

Perimeter=$4\sqrt6$ inches Area=$5$ square inches

Work Step by Step

Perimeter is the sum of the lengths of the sides. For a rectangle, $P=2w+2l$. $P=2(\sqrt6+1)+2(\sqrt6-1)$ Use the distributive property to simplify. $P=2\sqrt6+2+2\sqrt6-2$ Combine like radicals. $P=4\sqrt6$ The area of a rectangle is the product of the length and width. $A=l\times w$ $A=(\sqrt6+1)(\sqrt6-1)$ Use the FOIL method to multiply the two binomials. $A=(\sqrt6\times\sqrt6)+(-1\times\sqrt6)+(1\times\sqrt6)+(-1\times1)$ Simplify. $A=6-\sqrt6+\sqrt6-1$ Combine like radicals/like terms. $A=5$
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