1) How do the dimensions of garden B compare to the original garden?

Question

Original garden A: f(x)=x2

Garden B: A(x)= x2 +8x+7

Garden C: A(x)= x29

Garden D: A(x)= x213x+36

1) How do the dimensions of garden B compare to the original garden?

2) How do the dimensions of garden C compare to the original garden?

3) Is the total area of garden C more or less than the area of the original garden? EXPLAIN.

4) If the original garden was 12ft 12ft, what are the dimensions of garden D?

Answer 1

Dear student, I would say there are some notation to be clarified, e.g. x2 supposedly means the square

of x, x^2. Also the dimensions means the two values: length L(x) (horizontal) and width W(x) (vertical) sides

of the rectangular garden. The area A(x) = alone cannot precisely tell the length and width but I suppose

1) Garden A is x by x (unit, foot here)

Garden B is (x+7) by (x+1) or the other way

So the dimensions of Garden B are 7 and 1 unit(s) longer than Garden A.

2) The given A(x) for Garden C is not clear. To be factorable, I can only assume it is

A(x) = x^2-9 =(x+3)(x-3). L(x) = x+3, W(x) =x-3 (or the other way).

So compared to Garden A, the dimension of Garden C is 3 units longer in one side and 3 units less in the other.

3) The difference of areas of Garden C over Garden A is (x^2-9)-x^2 = -9. Garden C has 9 sq. unit less than Garden A in area.

4) I suppose A(x) for Garden D is A(x) = x^2 + 13x +36.= (x+9)(x+4). Now x is 12 ft, so the length and width of Garden D are (supposedly) 12+9=21 and 12+4 = 16 ft respectively.