Answer:
Step-by-step explanation:
Perimeter is
P = 2L + 2W.  We are given the perimeter as 180 feet, so
180 = 2L + 2W.  Solve this for either L or W.  I chose W, no reason...
180 - 2L = 2W so
90 - L = W  Hold that thought.  We'll come back to it in a minute.
Area is
A = LW.  We are given the area as 1800 square feet, so
1800 = LW.  Sub in 90 - L for W:
1800 = L(90 - L).  Distribute to get a quadratic:

Get everything on one side and solve for the length by factoring:

Factor this however you like to factor quadratics, to get the length of 
L = 30 and L = 60.  First off, the length is longer than the width in general, so if we want to solve for the width, plug in 60 as L in the equation in bold print:
90 - 60 = W and
30 = W
So L = 60 and W = 30