# Chapter 8 - Section 8.3 - Operations with Radicals - Exercise Set - Page 592: 90

Perimeter=$4\sqrt7$ inches Area=$6$ square inches

#### Work Step by Step

Perimeter is the sum of the lengths of the sides. For a rectangle, $P=2w+2l$. $P=2(\sqrt7+1)+2(\sqrt7-1)$ Use the distributive property to simplify. $P=2\sqrt7+2+2\sqrt7-2$ Combine like radicals. $P=4\sqrt7$ The area of a rectangle is the product of the length and width. $A=l\times w$ $A=(\sqrt7+1)(\sqrt7-1)$ Use the FOIL method to multiply the two binomials. $A=(\sqrt7\times\sqrt7)+(-1\times\sqrt7)+(1\times\sqrt7)+(-1\times1)$ Simplify. $A=7-\sqrt7+\sqrt7-1$ Combine like radicals/like terms. $A=6$

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