# Math

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Gina has 24 feet of fence, she wants to make the largest rectangular area possible for her rabbit to play in , what length should she make each side of the rabbit penn?

• Math -

That is calculus question.

a = length

b = width

P = Perimeter

A = Area

P = 2 a + 2 b = 2 ( a + b )

24 = 2 ( a + b ) Divide both sides by 2

12 = a + b

a + b = 12 Subtract a to both sides

a + b - a = 12 - a

b = 12 - a

A = a * b = a * ( 12 - a )

A = 12 a - a ^ 2

The function has a minimum value if f ' ( A ) = 0

and f " ( A ) = a positive number.

The function has a maximum value if f '( A ) = 0

and f ''( A ) = a negative number.

f ´ ( A ) = 12 - 2 a

f " ( A ) = - 2

f´ ( A ) = 0

12 - 2 a = 0 Add 2 a to both sides

12 - 2 a + 2 a = 0 + 2 a

12 = 2 a Divide both sides by 2

6 = a

a = 6 m

f´ ( A ) = 0

f " ( A ) = - 2

That is a maximum value.

b = 12 - a = 12 - 6 = 6 m

Square 6 x 6 m

• Math -

How do I figure out the largest rectangle area

• Math -

you solve it

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