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?
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 Ask the House
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February 2023
