Algebraic equation question

A rectangular field beside a river is to be fenced with 120m of fencing material. No fence is needed along the river bank.

By letting x represent the width of the field, how do you express the length of the field in terms of x?

And what dimensions should the field be to produce the maximum area?

Let l = length of the field
=> l + 2x = 120
=> l = 120 - 2x
Area, A = x * l = x * (120 - 2x)
For Area to be maximum, dA/dx = 0 and d^2A/dx^2 < 0
dA/dx = 0
=> 120 - 4x = 0
=> x = 30 m
d^2A/dx^2 = - 4 < 0
=> dimensions of the field should be
width, x = 30 m and
length, l -= 120 - 2x = 120 - 2*30 = 60 m.

Edit:
Algebraic method to find maximum area is as under.
A = x (120 - 2x)
= 120x - 2x^2
= 2(60x - x^2)
= 2 [(30)^2 - (x - 30)^2]
=> A is maximum, when x = 30
and maximum area = 2 * (30)^2 = 1800 m^2
=> l * x = 1800
=> l = 1800/30 = 60 m.

Length of the field is 120-2x.
Biggest area is obtained with x equals 30m and the length 60m.