# Chapter 10 - Radical Expressions and Equations - 10-1 The Pythagorean Theorem - Standardized Test Prep: 44

20

#### Work Step by Step

The area of the garden is 16x12. The area of the entire field is (16+2x)x(12+2x). Write an equation showing that the area of the garden is 60% of (times) the are of the field. $16\times12=0.6(16+2x)(12+2x)\longrightarrow$ multiply $192=0.6(16+2x)(12+2x)\longrightarrow$ divide each side by 0.6 $192\div0.6=0.6(16+2x)(12+2x)\div0.6\longrightarrow$ divide $320=(16+2x)(12+2x)\longrightarrow$ multiply the binomials $320=192+56x+4x^2\longrightarrow$ subtract 320 from each side $320-320=192+56x+4x^2-320\longrightarrow$ subtract $0=4x^2+56x-128\longrightarrow$ multiply each side by $\frac{1}{4}$ $0\times\frac{1}{4}=\frac{1}{4}(4x^2+56x-128)\longrightarrow$ multiply using the distributive property $0=x^2+14x-32\longrightarrow$ factor the trinomial; the factors of -32 that sum to 14 are -2 and 16 $0=(x+16)(x-2)\longrightarrow$ one of the 2 factors must be 0 $x+16=0$ or $x-2=0$ $x=-16$ or $x=2$ x cannot be negative, so x=2 The length of the longest side is $16+2x=16+2(2)=16+4=20.$

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