What will be the dimensions?

A dog trainer has 116 ft of fencing that will be used to create a rectangular work area for dogs. If the trainer wants to enclose an area of 720 ft², what will be the dimensions of the work area?

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x = width
y = length

xy = 720 {area of a rectangle is length x width}
2x + 2y = 116 {perimeter of a rectangle is 2(width) + 2(length)}

Take the second equation and divide each side by 2:
x + y = 58 {divided each side of second equation by 2}
​y = -x + 58 {subtracted x from each side}

xy = 720 {first equation, above}
x(-x + 58) = 720 {substituted (-x + 58), in for y, into xy = 720}
-x² + 58x = 720 {used distributive property}
x² - 58x + 720 = 0 {added x² and subtracted 58x from each side}
(x - 40)(x - 18) = 0 {factored into two binomials}
x - 40 = 0 or x - 18 = 0 {set each factor equal to zero}
x = 40 or x = 18 {solved each equation}

Using x = 18,
xy = 720
18y = 720 {substituted 18, in for x, into xy = 720}
y = 40 {divided each side by 40}

width = 18 ft
length = 40 ft

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