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Two Area Questions

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The length of a garden is three more than twice its width. If the area of the garden is 1,200 square feet, what is the perimeter of the garden. (An answer within 1 foot of the correct answer).

Hannah has 2000 feet of fence. She is going to make a rectangular garden using the fence and her barn for one side (so she only needs fencing on three sides of the garden). What is the largest area she can enclose? [Answer with just the number of square feet of area].

Jul 10, 2018

#1
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Let the width of the garden = W, then:

The length of the garden =2W + 3

Area = L x W

1,200 =W x (2W + 3)

W =23.756 - feet the width of the garden

2 x 23.756 + 3 =50.512 - feet the length of the garden

Perimeter = 2[L + W]

= 2[50.512 + 23.756]

=148.536

=~149 feet

Jul 10, 2018
#2
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Hannah has 2000 feet of fence. She is going to make a rectangular garden using the fence and her barn for one side (so she only needs fencing on three sides of the garden). What is the largest area she can enclose? [Answer with just the number of square feet of area].

Let  two  equal sides of the fence  =  S

Then the remaining side  (opposite the barn)   is   just  2000  - 2S

So....the area, A,   is just

A  = S (2000 - 2S)    simplify

A  = 2000S  - 2S^2         take the derivative of this and set to 0

A'  = 2000 - 4S  = 0

Solving, we have

2000  - 4S  = 0      add 4S  to both sides

2000  = 4S   divide both sides by 4

500  = S

So....the max area  is  S  (2000 - 2S)   =      500 ( 2000 - 2*500)   =   500 (1000)  =   500,000  ft^2   Jul 10, 2018
edited by CPhill  Jul 11, 2018