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September 30, 2014

Posted by **Marysvoice** on Monday, February 18, 2008 at 9:34am.

What should the dimensions of the garden be to give this area? 40ft is given so I answered with 40x20?

Is this correct?

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**Reiny**, Monday, February 18, 2008 at 9:39amYour answer is correct, but how did you set it up?

Did you use Calculus?

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**Marysvoice**, Monday, February 18, 2008 at 9:49amI am working with quadratic equations this week. Honestly, I drew a picture and made a logical guess.

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**Damon**, Monday, February 18, 2008 at 9:59amx = length

z = width

2x + 2 z = 80

x+z = 40

Area = y = x z

so

y = x (40-x)

x^2 - 40 x = -y

that is a parabola, max or min at vertex (assume you do not do calculus but do know "completing the square", do so.

x^2 - 40 x + 20^2 = -y + 400

(x-20)^2 = - (y-400)

so, parabola sheds water (y small when x big positive or negative.

vertex - the maximum - at x = 20

then y = 20

(sure enough, a square)

at that vertex, y, the area is sure enough 400

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**Marysvoice**, Monday, February 18, 2008 at 10:07amSo I am wrong? It is 400 instead of 800 sq ft?

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**Damon**, Monday, February 18, 2008 at 10:17amalways check.

20 + 40 + 20 + 40 = 120

You would have to stretch that 80 feet of fencing pretty hard.

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- Math typo -
**Damon**, Monday, February 18, 2008 at 10:06amvertex - the maximum - at x = 20

then z = 20

because x + z = 40

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**Damon**, Monday, February 18, 2008 at 10:15amif it were 40 by 20, the perimeter would be:

40 + 20 + 40 + 20 = 120

But you only have 80 feet of fence.

- Whoa - sorry, missed the barn -
**Damon**, Monday, February 18, 2008 at 10:40amI overlooked the barn being one side

perimeter = 2 x + z = 80

so z = 80 - 2 x

y = x z

y = x (80 - 2 x)

y = -2 x^2 + 80 x

2 x^2 - 80 x = -y

x^2 - 40 x = -y/2

x^2 - 40 x + 20^2 = -y/2 + 400

(x-20)^2 = - (y/2 - 400)

so x = 20

z = 80-40 = 40

area

y/2 = 400

y = area = 800

You guessed it right. I left out the wall of the barn.

- Whoa - sorry, missed the barn -
**Reiny**, Monday, February 18, 2008 at 11:57amLOL

Gives new meaning to the expression:

"Couldn't hit the side of a barn door...."

- Whoa - sorry, missed the barn -

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