A rectangular field has dimensions of (2x-3) yards and (x+4) yards. the area of the field is 285 square yards. what are the length and width of the field?

Area = Length x Width

285 = (2x-3) (x+4)

285 = 2x^2 + 8x - 3x - 12

285 = 2x^2 + 5x - 12

2x^2 + 5x - 12 = 285

2x^2 + 5x - 297 = 0

(2x^2 + 27) (x - 11) = 0

x = - 27/2 (rejected, length cannot be negative) or 11

x = 11

2x - 3 = 2 (11) - 3 = 19

x + 4 = 11 + 4 = 15

So the length and width are 19 yards and 15 yards