Posted by **Jane** on Tuesday, December 4, 2012 at 5:01pm.

Peter has 1200 yards of fencing to enclose a rectangular area. Find the dimensions of the rectangle that maximize the enclosed area?

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**Ms. Sue**, Tuesday, December 4, 2012 at 5:06pm
It's a square.

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**Jane**, Tuesday, December 4, 2012 at 5:15pm
So what exactly would the answer be? im confused..

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**Ms. Sue**, Tuesday, December 4, 2012 at 5:19pm
1200/4 = 300 yards on each side.

A = 300 * 300

A = ?

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**Jane**, Tuesday, December 4, 2012 at 5:20pm
Oh i see now! Ok thank you!

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**A.**, Tuesday, December 4, 2012 at 5:26pm
Finding the Absolute Area....

Area of the fence:

A=x*y

Perimeter of the fence

2x+2y=1200

Then, you solve for one variable

2x=1200-2y

x=600-y <-- plug this back into the Area function and you will get

A=(600-y)y

A=600y-y^2

And I believe you can set that equal to zero

-y^2+600y=0

Then you use the quadratic formula

b=600

a=-1

so y= -600/(2)*(-1)

y=300

That'll give you one side, then plug it back to perimeter equation to get x. Hope this is right!

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**Ms. Sue**, Tuesday, December 4, 2012 at 5:32pm
You're welcome.

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