Find the width and length

A dog trainer has 92 ft of fencing that will be used to create a rectangular work area for dogs. If the trainer wants to enclose an area of 360 ft², what will be the dimensions of the work area?

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x = width
y = length

xy = 360 {area of a rectangle is length x width}
2x + 2y = 92 {perimeter of a rectangle is 2(width) + 2(length)}

Take the second equation and divide each side by 2:
x + y = 46 {divided each side of second equation by 2}
​y = -x + 46 {subtracted x from each side}

xy = 360 {first equation, above}
x(-x + 46) = 360 {substituted (-x + 46), in for y, into xy = 360}
-x² + 46x = 360 {used distributive property}
x² - 46x + 360 = 0 {added x² and subtracted 46x from each side}
(x - 36)(x - 10) = 0 {factored into two binomials}
x - 36 = 0 or x - 10 = 0 {set each factor equal to zero}
x = 36 or x = 10 {solved each equation}

Using x = 10,
xy = 360
10y = 360 {substituted 10, in for x, into xy = 360}
y = 36 {divided each side by 10}

width = 10 ft
length = 36 ft

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