area=legnth times width
legnth is 1 less than 2 times width
l=legnth
w=width
l=-1+2w
l=2w-1
area=lw
area=45
subsitute
45=lw
45=(2w-1)w
distribute
45=2w^2-w
subtract 45 from both sides
0=2w^2-w-45
factor because if we have xy=0 and we factor we can assume that x and/or y=0 so
trial and error factor
0=(2w+9)(w-5)
set each to zero
0=2w+9
subtract 9
-9=2w
divide 2
-4.5=w
impossible since width cannot be negative so discard
w-5=0
add 5 to both sides
w=5
true
subsitute
l=2w-1
l=2(5)-1
l=10-1
l=9
w=5 cm
l=9 cm
