Exercise 46 Page 61

Use the difference of squares pattern, a^2-b^2=(a-b)(a+b).

16 ft by 32 ft

Practice makes perfect

Let say x be the number of feet by which Zelda decreases one dimension. She also increases the other dimension by x as shown below.

The dimensions of new deck are 24-x and 24+x. Given that its area is 512 square feet, we can find the dimensions. (24-x)(24+x)=512 To find x, we will use difference of squares pattern.

(24-x)(24+x)=512

ExpandDiffSquares

(a+b)(a-b)=a^2-b^2

24^2-x^2=512

CalcPow

Calculate power

576-x^2=512

SubEqn

LHS-512=RHS-512

64-x^2=0

We get another difference of squares. We will now factor it and apply the Zero Product Property.

64-x^2=0

FacDiffSquares

a^2-b^2=(a+b)(a-b)

(8+x)(8-x)=0

ZeroProdProp

Use the Zero Product Property

lc8+x=0 & (I) 8-x=0 & (II)

SubEqn

(I): LHS-8=RHS-8

lx=- 8 8-x=0

AddEqn

(II): LHS+8=RHS+8

lx_1=- 8 x_2=8

Since length cannot be negative, x=8. Therefore, the length is 32 ft and the width is 16 ft. Length: & 24+8=32 ft Width: & 24-8=16 ft

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Exercises p.60-63

Exercise 46 Page 61

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