After figuring out a common difference in this pattern, we can get further terms in the pattern:
1, -2, 2, -4, 0, -3, -1
Remember that the area of a rectangle is the length of the rectangle multiplied by the width of the rectangle.
In this case, we could say (where
is the area of the rectangle):

Substituting the values the problem gave us for
and
, we can find the formula for
in terms of
, which is:

The formula for the area of the rectangle would be A(x) = 10x³ - 20x² + 65x.
Area=1/2 times base times height
note:bh=base times height
a=1/2bh
b=width
h=-4+2w
h=2w-4
subsitute
a=1/2w(2w-4)
a=1/2(2s^2-4w)
a=w^2-2w
a=63
63=w^2-2w
subtract 63 from both sdies
0=w^2-2w-63
factor
find what 2 numbers multiply to get -63 and add to get -2
the numbers are -9 and 7
so
0=(w-9)(w+7)
if xy=0 then x and/or y=0
so
w-9=0
w+7=0
solve each
w-9=0
add 9 to both sdies
w=9
w+7=0
subtract 7 from both sides
w=-7
width cannot be negative so this can be discarded
width=9
subsitute
l=2w-4
l=2(9)-4
l=18-4
l=14
legnth=14 in
width/base=9 in
A is the correct answer you are looking for
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