Let L = lengthLet W = width Length is 5 yd less than twice the width ==> L = 2*W - 5 Area is 52 yd^2 ==> 52 = L*W Substitute the value for L from the 1st equation into the 2nd equation 52 = (2*W - 5) * W52 = 2*W^2 - 5*W0 = 2*W^2 - 5*W - 52 0 = (2W - 13)*(W + 4) 2W - 13 = 0 or W + 4 = 0W = 13/2 or W = -4 Width cannot be negative so discard W = -4 W = 13/2 ==> L = 2*(13/2) - 5 = 13 - 5 = 8 So the width is 13/2 yards and the length is 8 yards Check: 2*(13/2) - 5 = 13 - 5 = 8 (13/2)*8 = 4*13 = 52 yd^2
