If I have a garden that is square with sides of length x feet and next spring I plan to make it rectangular by lengthening one side 3 feet and shortening the other side by 3 feet.
Find a polynomial A(x) that represents the new area.
By how much will the area of the new garden differ from that of the old garden?
Old garden : x by x or x^2
new garden :(x-3) by (x+3)
A(x) = (x+3)(x-3) or x^2 - 9
difference = old garden - new garden
= x^2 - (x^2 - 9)
= 9
Thanks a lot. This really helps me understand the problem better. Hope I can help someday! :)
well the answer is 142
To find the polynomial A(x) that represents the new area, we need to express the dimensions of the new rectangular garden in terms of x.
Given that the sides of the original square garden have length x, the length of the new rectangular garden will be (x + 3) feet (increased by 3 feet), and the width will be (x - 3) feet (shortened by 3 feet).
The area of a rectangular garden is given by the formula A = length * width. Therefore, the area of the new garden, A(x), can be expressed as:
A(x) = (x + 3)(x - 3)
Simplifying the expression, we have:
A(x) = (x^2 - 9)
Now, let's calculate the difference in area between the new garden and the old garden.
The area of the old garden (square) can be expressed as A_old = x^2.
The difference in area between the new and the old garden is given by:
ΔA = A(x) - A_old
= (x^2 - 9) - x^2
= -9
So, the area of the new garden will differ from that of the old garden by -9 square feet.