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?
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 Ask the House
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February 2023
