A gardener has 60 feet of fencing with which to enclose a garden adjacent to a long existing wall. The gardener will use the wall for one side and the available fencing for the remaining three sides.

(a) If the sides perpendicular to the wall have length x feet, which of the following represents the area A of the garden?
A(x) = –2x2 + 30x
A(x) = –2x2 + 60x
A(x) = x2 – 60x
A(x) = 2x2 – 60x

Online "^" indicates an exponent.

Area = length * width

If x = length of each of the two sides, then the width = 60 - 2x

Thus the area = x(60-2x) = 60x - 2x^2

Unless you have a typo, I would not pick any of the choices.

To find the area A of the garden, we need to express it in terms of x, the length of the sides perpendicular to the wall.

Given that the gardener has 60 feet of fencing to enclose three sides of the garden, we know that the sum of the lengths of these three sides is 60.

Let's break it down:

- One side is the long existing wall, which doesn't require any additional fencing.
- The other two sides, perpendicular to the wall, have lengths x each.

Adding up the lengths:
x + x = 2x

Now we know that 2x + the length of the wall = 60. Rearranging this equation:
2x + w = 60
where w represents the length of the wall.

Since the wall is already present and doesn't require any fencing, the equation simplifies to:
2x = 60

Solving for x:
2x = 60
x = 30

Now we have the value of x, which is 30.

To find the area A of the garden, we need to calculate the product of the two perpendicular sides:
A = x * w

Since one side is x and the other side is the wall, which we don't know the exact length of, we can't express it as a single value. So the area A of the garden cannot be represented by any of the given options.