algebra 2 - h question

in order to save on fencing material, collins decided to construct his rabbit pen so that the side of the garage acts as one side of the pen. this way she only needs to fence the other three sides. if she starts with 100 ft of fencing, what are the dimensions of the rabbit pen with the maximum area?

The dimensions are 25 * 50 feet.

Step-by-step explanation:

The 3 sides of the pen will measure (2x + y) feet where x is the width and y is the length.

2x + y = 100

y = 100 - 2x

The area A = xy = x(100 - 2x) ft^2.

Finding the maximum area.

A = x(100 - 2x)

A = 100x - 2x^2 Finding the derivative:

A' = 100 - 4x

For maximum value of A this equals zero:

100 - 4x = 0

4x = 100

x = 25 ft, so this is the width.

The length is 100 - 2(25) = 50 ft.

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