assuming the garden is rectangular, we have the following formula for area:

  A = l * w

where l is the length and w is the width

we know that the length is longer than the width by 9 ft, so

  l = w + 9

the total area is 70, giving the following formula for area:

  70 = (w+9)*w

     = w^2 + 9w

this yields the quadratic equation:

  w^2 + 9w - 70 = 0

applying the quadratic formula, we have these two equations:

  w = (-9+sqrt[9^2 - 4(-70)])/2.

  w = (-9-sqrt[9^2 - 4(-70)])/2.

giving the solution set w = {5, -14}

since we know the width is a positive number, w = 5

  l = w + 9 = 14

the length of the garden is 14 feet, its width is 5 feet