Answer
The lot's dimensions are
length $ =80\; ft $
width $ = 50 \; 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= 260\; feet $.
therefore $ 2(l+w)=260 $
Isolate $ l $
$ l+w=130 $
$ l=130-w $ ... (1)
Cost along the lot's length $ =\$ 16 $ per foot.
Total cost along the lot's length $ 16l $.
Cost along the lot's two side widths $ =\$ 5 $ per foot.
Total cost along the two side widths $ = 5\times 2w =10w $.
Total cost of the fencing along the three sides $ =16l+10w $.
In the question we have total cost $\$ 1780 $.
Equate both.
$ 16l+10w=1780 $
Substitute the value of $ l $ from equation (1).
$ 16(130-w)+10w=1780 $
$ 2080-16w+10w=1780 $
$ -6w=1780-2080 $
$ -6w=-300 $
$ w=50 $ Substitute into equation (1).
$ l=130-50 $
$ l=80 $.
