Question

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?

Answer 1

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