Answer
The lot's dimensions are
Length $= 70 \; ft $
width $=40 \; ft $.
Work Step by Step
Perimeter of rectangular region is $ P=2(l+w) $.
where, $l $ is length and $ w $ is width.
In the question we have $ P= 220\; feet $.
therefore $ 2(l+w)=220 $
Isolate $ l $
$ l+w=110 $
$ l=110-w $ ... (1)
Cost along the lot's length $ =\$ 20 $ per foot.
Total cost along the lot's length $ 20l $.
Cost along the lot's two side widths $ =\$ 8 $ per foot.
Total cost along the two side widths $ = 8\times 2w =16w $.
Total cost of the fencing along the three sides $ =20l+16w $.
In the question we have total cost $\$ 2040 $.
Equate both.
$ 20l+16w=2040 $
Substitute the value of $ l $ from equation (1).
$ 20(110-w)+16w=2040 $
$ 2200-20w+16w=2040 $
$ -4w=2040-2200 $
$ -4w=-160 $
$ w=40 $ Substitute into equation (1).
$ l=110-40 $
$ l=70 $
