You have 188 feet of fencing to enclose a rectangular region. What is the maximum area?

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You have 188 feet of fencing to enclose a rectangular region. What is the maximum area?

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Answer 1 · 2016-04-09T00:38:59

$2209$ $2209$ square feet

Explanation:

$1$ $1$ . Make "let" statements to represent the length and width of the rectangular region.

Let $x$ $x$ represent the length.
Let $\frac{188 - 2 x}{2} = 94 - x$ $(188-2x)/2=94-x$ represent the width.

$2$ $2$ . Create an algebraic expression represent the area of a rectangle.

$A_{rectangle} = x (94 - x)$ $A_"rectangle"=x(94-x)$

$3$ $3$ . Complete the square.

$A_{rectangle} = 94 x - x^{2}$ $A_"rectangle"=94x-x^2$

$A_{rectangle} = - (x^{2} - 94 x)$ $A_"rectangle"=-(x^2-94x)$

$A_{rectangle} = - (x^{2} - 94 x + {(- \frac{94}{2})}^{2} - {(- \frac{94}{2})}^{2})$ $A_"rectangle"=-(x^2-94x+(-94/2)^2-(-94/2)^2)$

$A_{rectangle} = - {(x - 47)}^{2} + 2209$ $A_"rectangle"=-(x-47)^2+2209$

$:.$ , the maximum area of the rectangular region is $2209$ square feet.

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You have 188 feet of fencing to enclose a rectangular region. What is the maximum area?

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