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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.

25 ・50

Step-by-step explanation:

50 ft

the smallest possible measurement of the width is 14 feet

step-by-step explanation:

let's assume length of parallelogram is 'l'

width of parallelogram is 'w'

the perimeter of a parallelogram must be no less than 40 feet

so, we get

we are given

length of parallelogram is 6 feet

so,

l=6

we can plug it

now, we can solve for w

subtract both sides by 12

divide both sides by 2

and we get

so,

the smallest possible measurement of the width is 14 feet

whats the question?

step-by-step explanation: