Suppose you have 54 feet of fencing to enclose a rectangular dog pen. the function a=27x-x^2 , where x = width, gives you the area of the dog pen in square feet. what width gives you the maximum area? what is the maximum area? round to the nearest tenth as necessary.width = 13.5 ft; area = 182.3 ft^2width = 27 ft; area = 182.3 ft^2width = 13.5 ft; area = 546.8 ft^2width = 27 ft; area = 391.5 ft^2

Given function: A=27x-x^2 , where x = width, gives you the area of the dog pen in square feet.

The given function is a quadratic function.

And a quadratic function represents a parabola.

The top most point of the parabola is called vertex.

So, we need to find the x-coordinate of the vertex to find the width that gives you the maximum area. Because x represents the width of the rectangle.

A=27x-x^2 could be written in standard form A= -x^2+27x.

We know formula for x-coordinate of the vertex = -b/2a.

For the given function A= -x^2+27x, a=-1 and b=27.

Plugging values in the formula, we get

x-coordinate of the vertex = -b/2a = -27/2(-1) = 27/2 = 13.5 feet.

Plugging x=13.5 in given function, we get

A= -(13.5)^2+27(13.5)

= -182.25 +364.5 = 182.25 ≈ 182.3.

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step-by-step explanation:

told you

what is the question? i am guessing you are looking for the area.

to find an area, you have to do length x width.

in this case, it would be 12 ft x 4 ft = 48 sq. ft